]> 2026-06-23T12:50:17+00:00 Normal subgroup 0 en tabular 1 Term invariant under inner automorphisms, self-conjugate subgroup same left and right cosets kernel of a homomorphism subgroup that is a union of conjugacy classes 2024-12-02T06:22:01Z 2460646.7652894 Normal subgroup 0 Normal subgroup#DummitFoote;82;formal definition 82 formal definition 0 Normal subgroup#Herstein;50;Section 2.6;formal definition 50 Section 2.6 formal definition 0 Normal subgroup#Hungerford;41;Section 1.5;definition introduced through proposition 41 Section 1.5 definition introduced through proposition 0 Normal subgroup#Lang;14;definition in paragraph 14 definition in paragraph 0 Normal subgroup#Artin;52;Point (4.8);formal definition 52 Point (4.8) formal definition 0 Normal subgroup#CohnBasicAlgebra;27;Section 2.1;definition in paragraph 27 Section 2.1 definition in paragraph 0 Normal subgroup#SchaumsGT;111;formal definition 111 formal definition 0 Normal subgroup#AlperinBell;6;definition in paragraph 6 definition in paragraph 0 Normal subgroup#RobinsonGT;15;Proposition 1.3.15;definition introduced through proposition 15 Proposition 1.3.15 definition introduced through proposition 0 Normal subgroup#RotmanGT;30;formal definition 30 formal definition 0 1 plainlist 2 [[Definition style::tabular]] Normal subgroup# QUERYa06e7f16fa3dc8cb712b7a1b798724eb 0 1 table 2 [[Defining ingredient::Normal subgroup]] Normal subgroup# QUERY1548e7086b25ae3039e93edfe01803a3 0 2 table 5 [[Fact about:: <q>[[Page::Normal subgroup]] [[Number::1]]</q> ]] Normal subgroup# QUERYbbbbb955b4cf4921ff4b37b8d3353bb7 0 2 table 3 [[Fact about.Page::Normal subgroup]] Normal subgroup# QUERY6d61cc9dfc328b3215ccf3f1811ffc7d 0 1 table 2 [[Survey article about::Normal subgroup]] Normal subgroup# QUERY07b226f9c6c39c64f9ac540dea10ac74 0 2 plainlist 3 [[Survey article about.Defining ingredient::Normal subgroup]] Normal subgroup# QUERY2e68bda4a90932d8553fb806d38e8522 0 1 plainlist 2 [[Analogue of::Normal subgroup]] Normal subgroup# QUERY9f4fb79df87e0a491678c503b273b28e 0 1 plainlist 2 [[Variation of::Normal subgroup]] Normal subgroup# QUERYb699f166b06e463c2cbd7d5cf242dcd7 0 1 plainlist 2 [[Opposite of::Normal subgroup]] Normal subgroup# QUERY4fb725b3eb69fd5cba1ca425950c736a 0 2 plainlist 4 [[Fact about.Page::Normal subgroup]] [[Category:Subgroup property implications]] Normal subgroup# QUERYa65ca9b902546984febfb36064ff01f6 0 2 plainlist 4 [[Fact about.Page::Normal subgroup]] [[Category:Subgroup property non-implications]] Normal subgroup# QUERY35106e2e37306552d0e5aa04827bf049 0 2 plainlist 4 [[Fact about.Page::Normal subgroup]] [[Category:Subgroup metaproperty satisfactions]] Normal subgroup# QUERYcf93134b8e71aa05fea57c876e991702 0 2 plainlist 4 [[Fact about.Page::Normal subgroup]] [[Category:Subgroup metaproperty dissatisfactions]] Normal subgroup# QUERYd2277e8bf85a0a2a791aa21365bbad6f 0 2 plainlist 4 [[Fact about.Page::Normal subgroup]] [[Category:Subgroup property satisfactions]] [[Category:Subgroup property satisfactions]] [[Fact about.Page::Normal subgroup]] Normal subgroup# QUERY59f30cadfe4b9c2367c7861f44d735d3 0 2 plainlist 4 [[Fact about.Page::Normal subgroup]] [[Category:Subgroup property dissatisfactions]] [[Category:Subgroup property dissatisfactions]] [[Fact about.Page::Normal subgroup]] Normal subgroup# QUERYa86209a9fe4492552b6bae7cffcb8bee 0 1 plainlist 2 [[Uses property satisfaction of::Normal subgroup]] Normal subgroup# QUERYe18741ee3de0f61bb33b396f89399684 0 1 plainlist 2 [[Proves property satisfaction of::Normal subgroup]] Normal subgroup# QUERY13ca149f505d567fbee02c88d639b057 0 2 table 6 <q> <q>[[Satisfies property::Normal subgroup]]</q> OR [[Satisfies property.Stronger than::Normal subgroup]] [[Category:Particular subgroups]]</q> Normal subgroup# QUERY6d46b7fdf83e6e876c61cec0ca118d9d 0 2 table 6 <q> <q>[[Dissatisfies property::Normal subgroup]]</q> OR [[Dissatisfies property.Weaker than::Normal subgroup]] [[Category:Particular subgroups]]</q> Normal subgroup# QUERYb2356a6eb5487d6561d82a7bda8630b6 0 2 table 12 <q>[[Satisfies property::Normal subgroup]] [[Dissatisfies property::Characteristic subgroup]] [[Category:Particular subgroups]] OR [[Satisfies property.Stronger than::Normal subgroup]] [[Dissatisfies property.Weaker than::Characteristic subgroup]] [[Category:Particular subgroups]]</q> Normal subgroup# QUERY5e2655e13ad05870c73678d116507e6e 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Characteristic subgroup]] Normal subgroup# QUERY9c20fd8454bcc1441e1ba02d01c45f2f 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Characteristic subgroup]] Normal subgroup# QUERY4e47f44a59a6362fe976eceed7a72aad 0 1 plainlist 4 [[Satisfies property::Normal subgroup]] [[Dissatisfies property::Central factor]] Normal subgroup# QUERY7f0a6ea3f472fa68ccf29225a8dc6f68 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Central factor]] Normal subgroup# QUERY175162142d2ae54e4d6ba095195dbdce 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Central factor]] Normal subgroup# QUERY9c9acfe9753b6365a5beba8f9aa0976b 0 2 table 12 <q>[[Satisfies property::Normal subgroup]] [[Dissatisfies property::Direct factor]] [[Category:Particular subgroups]] OR [[Satisfies property.Stronger than::Normal subgroup]] [[Dissatisfies property.Weaker than::Direct factor]] [[Category:Particular subgroups]]</q> Normal subgroup# QUERY64e8ac10b8a5fca8cde5fc5371873559 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Direct factor]] Normal subgroup# QUERYa1d13db0bc160058c3c65df37407f360 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Direct factor]] Normal subgroup# QUERY833ebbb44e43a6dde476743570a09347 0 2 table 12 <q>[[Satisfies property::Normal subgroup]] [[Dissatisfies property::Central subgroup]] [[Category:Particular subgroups]] OR [[Satisfies property.Stronger than::Normal subgroup]] [[Dissatisfies property.Weaker than::Central subgroup]] [[Category:Particular subgroups]]</q> Normal subgroup# QUERY21b746331c958982f8121581e273b746 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Central subgroup]] Normal subgroup# QUERYdeaab161e5b4aa71e2757cd7a13ea6eb 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Central subgroup]] Normal subgroup# QUERY4fce6e7cbc4a28c28b877837427896f0 0 1 plainlist 4 [[Satisfies property::Normal subgroup]] [[Dissatisfies property::Fully invariant subgroup]] Normal subgroup# QUERY061ec3bd7e1010bd8f343860091216f5 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Fully invariant subgroup]] Normal subgroup# QUERY1ddef1eb011c223f2dd6d21c556259a8 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Fully invariant subgroup]] Normal subgroup# QUERY46b5b4b694ca950e466e8311ac33685a 0 1 plainlist 4 [[Satisfies property::Normal subgroup]] [[Dissatisfies property::Strictly characteristic subgroup]] Normal subgroup# QUERY8b1700f7dd958c8e97972631b0dfdf71 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Strictly characteristic subgroup]] Normal subgroup# QUERY0b7caf16bca790bd1be5262303a39e6e 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Strictly characteristic subgroup]] Normal subgroup# QUERYbb6774cc9f1eb9145e98118bffe9986d 0 1 plainlist 4 [[Satisfies property::Normal subgroup]] [[Dissatisfies property::Isomorph-free subgroup]] Normal subgroup# QUERYb8e195b0496a177a1c293948e63c342d 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Isomorph-free subgroup]] Normal subgroup# QUERY50af6403f1c389149472e7a59576a94d 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Isomorph-free subgroup]] Normal subgroup# QUERY1cd36abc05d5fab123541aca019f1994 0 1 plainlist 4 [[Satisfies property::Normal subgroup]] [[Dissatisfies property::Isomorph-containing subgroup]] Normal subgroup# QUERYf44174fceabf95569e10085dd8c42f60 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Isomorph-containing subgroup]] Normal subgroup# QUERY348244235aac33eb03b98d9743d4838e 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Isomorph-containing subgroup]] Normal subgroup# QUERY5b905fb30df8b39e6a9dd41e2152bb7f 0 1 plainlist 4 [[Satisfies property::Normal subgroup]] [[Dissatisfies property::Injective endomorphism-invariant subgroup]] Normal subgroup# QUERY40e017f74e985cbb568b3a66ea179590 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Injective endomorphism-invariant subgroup]] Normal subgroup# QUERY0d8e0ecf0ab6316667c9e84e79f0b6d5 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Injective endomorphism-invariant subgroup]] Normal subgroup# QUERY913c0e0e326a02410ff75091352ec0d5 0 2 table 12 <q>[[Satisfies property::Normal subgroup]] [[Dissatisfies property::Transitively normal subgroup]] [[Category:Particular subgroups]] OR [[Satisfies property.Stronger than::Normal subgroup]] [[Dissatisfies property.Weaker than::Transitively normal subgroup]] [[Category:Particular subgroups]]</q> Normal subgroup# QUERYd147b46253d9ca488d31df182e0dbf42 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Transitively normal subgroup]] Normal subgroup# QUERY858b61112bf5bade65ceaae847884101 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Transitively normal subgroup]] Normal subgroup# QUERY748606a75072daf9608a3fbad7f0582d 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Cocentral subgroup]] Normal subgroup# QUERY42ac06f91d1e0500f0563382442b6293 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Cocentral subgroup]] Normal subgroup# QUERY5f465e6453117310c354e575eee8be10 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::SCAB-subgroup]] Normal subgroup# QUERYc6d9ac2eb850bf4277ed51ffbfa401c0 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::SCAB-subgroup]] Normal subgroup# QUERYd585600cf8e0610605d7a62108016a8f 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Conjugacy-closed normal subgroup]] Normal subgroup# QUERY3b3dc8b891687b9e7ba4a6e3b1396c47 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Conjugacy-closed normal subgroup]] Normal subgroup# QUERY19a445265ece2a55b784fc083f45f48b 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Abelian-quotient subgroup]] Normal subgroup# QUERY5be1aec3de6b5b3566cc4f9b7625508b 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Abelian-quotient subgroup]] Normal subgroup# QUERY348f2ecfda328cdd36b3b2e8d71aca54 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Complemented normal subgroup]] Normal subgroup# QUERY07226e4e68933303132e164f45e0abc6 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Complemented normal subgroup]] Normal subgroup# QUERY75837d410a46d534ee0b62a3016bacc0 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Endomorphism kernel]] Normal subgroup# QUERYd0fee4ab3e3fd82ac1510ef8d8de732c 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Endomorphism kernel]] Normal subgroup# QUERY2fdcbba877128ec342c5f7ff1564c9ac 0 1 plainlist 2 [[Stronger than::Normal subgroup]] Normal subgroup# QUERY972e76d6041ceef4207b3efe282a6eb8 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Satisfies metaproperty::Transitive subgroup property]] Normal subgroup# QUERY1abd356b7235ade8dcb8ea077793268b 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Satisfies metaproperty::Intermediate subgroup condition]] Normal subgroup# QUERY15d197bc905c1dc6d3b3e7688ae985be 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Satisfies metaproperty::Transfer condition]] Normal subgroup# QUERYce1386ceceff6694b5023c889dbc557c 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Satisfies metaproperty::Quotient-transitive subgroup property]] Normal subgroup# QUERY9c63059a47b6003115cd048ea971dbd2 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Satisfies metaproperty::Intersection-closed subgroup property]] Normal subgroup# QUERY695667b2906321529bd65e881e2be47a 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Satisfies metaproperty::Join-closed subgroup property]] Normal subgroup# QUERY2c7d3aff54c4d95b5c794d5575d7a415 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Satisfies metaproperty::Trim subgroup property]] Normal subgroup# QUERY799bb80e9d0cfb3899b640c04e3c19d2 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Satisfies metaproperty::Inverse image condition]] Normal subgroup# QUERY17ecc2c444d3e27d87dbfb301ea7c779 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Satisfies metaproperty::Image condition]] Normal subgroup# QUERY83158f58f995d495f96596479df24259 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Satisfies metaproperty::Centralizer-closed subgroup property]] Normal subgroup# QUERYa8307302ac658a50ce8a112242ca9034 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Dissatisfies metaproperty::Transitive subgroup property]] Normal subgroup# QUERYe7e1d8a0cdab32b30b9da9833ecd778d 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Dissatisfies metaproperty::Intermediate subgroup condition]] Normal subgroup# QUERY08585614d84cf0aa91326a4794095376 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Dissatisfies metaproperty::Transfer condition]] Normal subgroup# QUERY77c83b47222e2fe0c7524d7140b9adfa 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Dissatisfies metaproperty::Quotient-transitive subgroup property]] Normal subgroup# QUERY0a71ef18d92ffd732a7b4b0c0981304d 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Dissatisfies metaproperty::Intersection-closed subgroup property]] Normal subgroup# QUERYcb0c5ef39b26d4bd6942ce38a8106df6 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Dissatisfies metaproperty::Join-closed subgroup property]] Normal subgroup# QUERY2865cc2543ed841ec84994c96ca4488a 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Dissatisfies metaproperty::Trim subgroup property]] Normal subgroup# QUERY4de746b0da09f52ba516d8395a93f931 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Dissatisfies metaproperty::Inverse image condition]] Normal subgroup# QUERYf5f8b53c39182d14d9bba5bfa8a60af6 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Dissatisfies metaproperty::Image condition]] Normal subgroup# QUERY2a33ee61e0a782a4c9421152fcb609ae 0 1 plainlist 4 [[Stronger than::Normal subgroup]] [[Dissatisfies metaproperty::Centralizer-closed subgroup property]] Normal subgroup# QUERYe91dd55def623296b0a0b75eed44b261 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Normal Sylow subgroup]] Normal subgroup# QUERYbb2e744c7f2d398de12df5d8dca34113 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Normal Sylow subgroup]] Normal subgroup# QUERY1381938f0dbe0c4fa5aa7026f8fa084e 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Normal Hall subgroup]] Normal subgroup# QUERYacebb6b1c353b5c3b4a0c7135e98e6dc 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Normal Hall subgroup]] Normal subgroup# QUERY37a49c0b7007c4ebb73e8a20c929d8be 0 1 plainlist 3 [[Category:Subgroup property conjunctions]] [[Conjunction involving::Normal subgroup]] Normal subgroup# QUERY223261f58598ba84a7be179fd0334f35 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Abelian normal subgroup]] Normal subgroup# QUERYa8da33c55c329912413a1a153f48e786 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Abelian normal subgroup]] Normal subgroup# QUERY29a0ad8e6dad7747a71d8cb316f00545 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Cyclic normal subgroup]] Normal subgroup# QUERYca8a74f6e3e9a9e2163cf76b334f2baf 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Cyclic normal subgroup]] Normal subgroup# QUERY88b0bfd83109a82cfe06938e03cd5142 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Solvable normal subgroup]] Normal subgroup# QUERY2a97f247c29be37dc27a1a779ec710d1 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Solvable normal subgroup]] Normal subgroup# QUERYef9b2582b4631210c475d3226c3e741e 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Nilpotent normal subgroup]] Normal subgroup# QUERY9ca760bcbbc6e6314271b8b5d47325a4 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Nilpotent normal subgroup]] Normal subgroup# QUERY03a91878cde4d3a260df5595f9c0aa3e 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Simple normal subgroup]] Normal subgroup# QUERY554ebfb701e0f17763dec1710f42a53a 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Simple normal subgroup]] Normal subgroup# QUERY503a92b72ebbf1eb9891afc0bbaac0e4 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Perfect normal subgroup]] Normal subgroup# QUERYe80a4404c8085d01f4c1e63d21e5385d 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Perfect normal subgroup]] Normal subgroup# QUERYc2f479a0b3db41ad2138f0bf97b380b7 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Finite normal subgroup]] Normal subgroup# QUERY54d9a3eb224284c2d9b3ef19c503d81f 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Finite normal subgroup]] Normal subgroup# QUERY61861fe68aef99971db130e62b22f5e7 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Periodic normal subgroup]] Normal subgroup# QUERY4e79cdd57a66b1561a88a07cb4935cef 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Periodic normal subgroup]] Normal subgroup# QUERY3f477c2e2959b5d4524c4810dd9be087 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Finitely generated normal subgroup]] Normal subgroup# QUERY69c6d02d2d7bafea432411eb6cd95d56 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Finitely generated normal subgroup]] Normal subgroup# QUERY1a95d0842b679bb77fc59c553387a884 0 1 plainlist 3 [[Category:Conjunctions of group property with subgroup property]] [[Conjunction involving::Normal subgroup]] Normal subgroup# QUERY6b25569d8bbbf36ecbba7a9be75c45ae 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Normal subgroup of finite group]] Normal subgroup# QUERYf31b827d451399b0deba55f5457fd5f2 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Normal subgroup of finite group]] Normal subgroup# QUERY42e63fb5864d588f05acfb6e69310494 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Normal subgroup of finitely generated group]] Normal subgroup# QUERY42ef17ccd05cd9e52e1b0ccc39f2d76f 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Normal subgroup of finitely generated group]] Normal subgroup# QUERY1155ad96fad2c05c80982ff94cfa4551 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Normal subgroup of periodic group]] Normal subgroup# QUERY55f688ccd869e22e621f589a647a08a1 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Normal subgroup of periodic group]] Normal subgroup# QUERY385b46d1b60be28ce9ad0bec2b265858 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Normal subgroup of group of prime power order]] Normal subgroup# QUERYfc004588ab0a495d5b5bd504fa0baea3 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Normal subgroup of group of prime power order]] Normal subgroup# QUERY34dafa8bc9526c108d034cfc1ff44d42 0 2 table 12 <q>[[Satisfies property::Subnormal subgroup]] [[Dissatisfies property::Normal subgroup]] [[Category:Particular subgroups]] OR [[Satisfies property.Stronger than::Subnormal subgroup]] [[Dissatisfies property.Weaker than::Normal subgroup]] [[Category:Particular subgroups]]</q> Normal subgroup# QUERYba3d8b8b615bf56d26809f01986bdec1 0 1 list 4 [[Stronger than::Subnormal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYf7b84f9f6d8ba202fe0c47045bdbe15f 0 1 broadtable 4 [[Stronger than::Subnormal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYf6020e1a3d6ec9e86245afacfe3cbb0c 0 2 table 12 <q>[[Satisfies property::Permutable subgroup]] [[Dissatisfies property::Normal subgroup]] [[Category:Particular subgroups]] OR [[Satisfies property.Stronger than::Permutable subgroup]] [[Dissatisfies property.Weaker than::Normal subgroup]] [[Category:Particular subgroups]]</q> Normal subgroup# QUERY55aafc6321a77d2e7ca455b7f40ef8db 0 1 list 4 [[Stronger than::Permutable subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYb3e6f92193abd8c20e9df538258c6fbf 0 1 broadtable 4 [[Stronger than::Permutable subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY46bd94f62db71cb511bd436cc764e155 0 2 table 12 <q>[[Satisfies property::2-subnormal subgroup]] [[Dissatisfies property::Normal subgroup]] [[Category:Particular subgroups]] OR [[Satisfies property.Stronger than::2-subnormal subgroup]] [[Dissatisfies property.Weaker than::Normal subgroup]] [[Category:Particular subgroups]]</q> Normal subgroup# QUERY2c85ce62eefbc2bcc8f9cb614e79c5cf 0 1 list 4 [[Stronger than::2-subnormal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY7e9c5f788a0f7f2578dbed6c93c4603a 0 1 broadtable 4 [[Stronger than::2-subnormal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY033f4b410f5566f6746c0de2b0b1da3c 0 1 list 4 [[Stronger than::3-subnormal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY2566d13d79d9cdc05837886ed4a45169 0 1 broadtable 4 [[Stronger than::3-subnormal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY100d1b2318d81792ec5c032df09da64e 0 1 list 4 [[Stronger than::4-subnormal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY7deaf8fa91ed565f47fa45a1b89729e8 0 1 broadtable 4 [[Stronger than::4-subnormal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYd8da476554f746be73d5f8681084c3c5 0 1 list 4 [[Stronger than::Ascendant subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYc3451cbc42097baaad049996e31433be 0 1 broadtable 4 [[Stronger than::Ascendant subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY48bb485361679b570e76fecb0f21e279 0 1 list 4 [[Stronger than::Descendant subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY10fbe0c8a2282f57f7a95e60fbdbe501 0 1 broadtable 4 [[Stronger than::Descendant subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYaf12fbaed01f0096df63af25c4531e55 0 1 list 4 [[Stronger than::Serial subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY41e0d4a6eb1ef60fee6f9bd85f84e2db 0 1 broadtable 4 [[Stronger than::Serial subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYbee8b7b09180c56fb6cca83812294843 0 2 table 12 <q>[[Satisfies property::Hypernormalized subgroup]] [[Dissatisfies property::Normal subgroup]] [[Category:Particular subgroups]] OR [[Satisfies property.Stronger than::Hypernormalized subgroup]] [[Dissatisfies property.Weaker than::Normal subgroup]] [[Category:Particular subgroups]]</q> Normal subgroup# QUERYef01a5eb7bd088f3987142fecda2f7c8 0 1 list 4 [[Stronger than::Hypernormalized subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYb8b9908e56ae17d3ffb40097e38cc780 0 1 broadtable 4 [[Stronger than::Hypernormalized subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYda606975cefba2901acf18a658cc5346 0 1 list 4 [[Stronger than::Finitarily hypernormalized subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYbe66a06fb6e4079bedad735f24290f60 0 1 broadtable 4 [[Stronger than::Finitarily hypernormalized subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY42e483b96490759e3acd21dbf044e48f 0 1 list 4 [[Stronger than::2-hypernormalized subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY70039e7a5d9f95620651e5b1d3f9d8b5 0 1 broadtable 4 [[Stronger than::2-hypernormalized subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYe5f83f1605204987e20e4d67a8ca1d44 0 2 table 12 <q>[[Satisfies property::Pronormal subgroup]] [[Dissatisfies property::Normal subgroup]] [[Category:Particular subgroups]] OR [[Satisfies property.Stronger than::Pronormal subgroup]] [[Dissatisfies property.Weaker than::Normal subgroup]] [[Category:Particular subgroups]]</q> Normal subgroup# QUERY8eeed09123e773f0f08ad10c7956346f 0 1 list 4 [[Stronger than::Pronormal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY3858b734ffa2c47da16698c4f10b9be8 0 1 broadtable 4 [[Stronger than::Pronormal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY74e70dcda0411658bd6dc56f6f9dc898 0 1 list 4 [[Stronger than::Weakly pronormal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYeb3721e34df7b73156ea17363d6397d2 0 1 broadtable 4 [[Stronger than::Weakly pronormal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY09ac5a92054e1d92deeb9954fd6d6da8 0 1 list 4 [[Stronger than::Paranormal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY5dde591c75e1d11356c2a9db1aaae92a 0 1 broadtable 4 [[Stronger than::Paranormal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYb33c58e5c9a0cfc049c6c51f3951e0bc 0 1 list 4 [[Stronger than::Weakly normal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYa8c9f5e486f7f24525d4b9849f6f1b69 0 1 broadtable 4 [[Stronger than::Weakly normal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYfc7a04251792845c1502070c5078db97 0 2 table 12 <q>[[Satisfies property::Intermediately subnormal-to-normal subgroup]] [[Dissatisfies property::Normal subgroup]] [[Category:Particular subgroups]] OR [[Satisfies property.Stronger than::Intermediately subnormal-to-normal subgroup]] [[Dissatisfies property.Weaker than::Normal subgroup]] [[Category:Particular subgroups]]</q> Normal subgroup# QUERY61ad1986d94491b40eef88047da2209c 0 1 list 4 [[Stronger than::Intermediately subnormal-to-normal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY4253ef2bef4696acaef54880205e0912 0 1 broadtable 4 [[Stronger than::Intermediately subnormal-to-normal subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY920741d2b9fccc848a0f1bce7e4a65f6 0 1 list 4 [[Stronger than::Conjugate-permutable subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYc9e4f5136feac1a62386504c043201a5 0 1 broadtable 4 [[Stronger than::Conjugate-permutable subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERYbedf548ed4f7153713de83a94754c2d8 0 1 list 4 [[Stronger than::Modular subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY80be5b90ac53f16544da80a3edc8b815 0 1 broadtable 4 [[Stronger than::Modular subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY4261b550c798d1c9420c18d2414c5acf 0 1 list 4 [[Stronger than::Automorph-permutable subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY0e1c371f32c64d1cde2f05a08674315c 0 1 broadtable 4 [[Stronger than::Automorph-permutable subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY9c4908ef1a550bacb758d083e6568d35 0 1 list 4 [[Stronger than::Elliptic subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY93a8c130d62ad68d7d4dd220c8f6318e 0 1 broadtable 4 [[Stronger than::Elliptic subgroup]] [[Weaker than::Normal subgroup]] Normal subgroup# QUERY9fce2396c5ae781f394bc3b1df94bb10 0 1 plainlist 2 [[Weaker than::Normal subgroup]] Normal subgroup# QUERY8b4c0e2bd505f26a6189004b530237da 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Satisfies metaproperty::Transitive subgroup property]] Normal subgroup# QUERY1436b423ce52e26a0108e07975b3cb18 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Satisfies metaproperty::Intermediate subgroup condition]] Normal subgroup# QUERY18b5b095dc81037e43a3e2edc2e56e68 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Satisfies metaproperty::Transfer condition]] Normal subgroup# QUERY796fc3fc74488edb080da442c5beee45 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Satisfies metaproperty::Quotient-transitive subgroup property]] Normal subgroup# QUERY9c2174940b8df2f53b944f8cefadd63d 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Satisfies metaproperty::Intersection-closed subgroup property]] Normal subgroup# QUERYc1fb6819c2aa071cbd27f1e602bffa2f 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Satisfies metaproperty::Join-closed subgroup property]] Normal subgroup# QUERYaf937d189458b8556e37a9880a8fd0f7 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Satisfies metaproperty::Trim subgroup property]] Normal subgroup# QUERY1769c40207644de88f578f16d6f6d086 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Satisfies metaproperty::Inverse image condition]] Normal subgroup# QUERY99eeca138eccaaad483a036089853cff 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Satisfies metaproperty::Image condition]] Normal subgroup# QUERY5ebcd1c9371e88f35438c6481278fbac 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Satisfies metaproperty::Centralizer-closed subgroup property]] Normal subgroup# QUERY8fe2b4fe70f257becbf43bdd488e3bc8 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Dissatisfies metaproperty::Transitive subgroup property]] Normal subgroup# QUERY84df9f57bad822c2e664ec1328618b12 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Dissatisfies metaproperty::Intermediate subgroup condition]] Normal subgroup# QUERYeaaea7bb3a025c0a4a9e7d779ed25551 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Dissatisfies metaproperty::Transfer condition]] Normal subgroup# QUERYac6517e4333dce3b23decd386ba067e0 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Dissatisfies metaproperty::Quotient-transitive subgroup property]] Normal subgroup# QUERYc96a6b8098983fefdeb0676f41b9c400 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Dissatisfies metaproperty::Intersection-closed subgroup property]] Normal subgroup# QUERY3c7870e2bd1371130c62efea2ba2078c 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Dissatisfies metaproperty::Join-closed subgroup property]] Normal subgroup# QUERY7521dcd7a0b80d77d6324a90f9380aa6 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Dissatisfies metaproperty::Trim subgroup property]] Normal subgroup# QUERYa15e37a19a626361c3d32db1453aa94f 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Dissatisfies metaproperty::Inverse image condition]] Normal subgroup# QUERY40d56ad677ce92ad4b4fb2b4f983f88e 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Dissatisfies metaproperty::Image condition]] Normal subgroup# QUERY3aa97823b7919aeca479277cf3adb77b 0 1 plainlist 4 [[Weaker than::Normal subgroup]] [[Dissatisfies metaproperty::Centralizer-closed subgroup property]] Normal subgroup# QUERY9eaaee73cae77655a6a06559853d99fd 0 1 plainlist 2 [[Satisfies metaproperty::First-order subgroup property]] Normal subgroup# QUERYace4cf8572382388dca598b4cd088d8c 0 1 plainlist 2 [[Satisfies metaproperty::Function restriction-expressible subgroup property]] Normal subgroup# QUERY6aa24c02f8e67de24223fa849790e0e6 0 1 plainlist 2 [[Satisfies metaproperty::Relation implication-expressible subgroup property]] Normal subgroup# QUERYda878a4b9f5ff2713c910190c3a8d6ad 0 1 plainlist 2 [[Satisfies metaproperty::GAP-testable subgroup property]] Normal subgroup# QUERYab3deb33606903472662717bd3ca61c2 0 1 plainlist 2 [[Satisfies metaproperty::GAP-listable subgroup property]] Normal subgroup# QUERYe6c7e410aa0a9124a787ec94e3720a50 0 1 plainlist 2 [[Satisfies metaproperty::GAP-codable subgroup property]] Normal subgroup# QUERY0db1d57349eaa4fa10fe190d719c5331 Derived subgroup 0 en Derived subgroup Center 0 en Center S3 in S5 0 en S3 in S5 S4 in S5 0 en S4 in S5 Center of dihedral group:D8 0 en Center of dihedral group:D8 Normality is strongly intersection-closed 0 en Normality is strongly intersection-closed Characteristic implies normal 0 en Characteristic implies normal Central implies normal 0 en Central implies normal Central factor implies normal 0 en Central factor implies normal Direct factor implies normal 0 en Direct factor implies normal Pronormal and subnormal implies normal 0 en Pronormal and subnormal implies normal Commutator of a group and a subgroup implies normal 0 en Commutator of a group and a subgroup implies normal Potentially verbal implies normal 0 en Potentially verbal implies normal Subgroup of index two is normal 0 en Subgroup of index two is normal Normal subsemigroup 0 en Normal subsemigroup Abelian normal subgroup 0 en Abelian normal subgroup Normality is strongly intersection-closed 0 en Normality is strongly intersection-closed Normal implies permutable 0 en Normal implies permutable Normal implies join-transitively subnormal 0 en Normal implies join-transitively subnormal Proper and normal in quasisimple implies central 0 en Proper and normal in quasisimple implies central Normal implies modular 0 en Normal implies modular Normalizer of a subgroup 0 en Normalizer of a subgroup Subnormal subgroup 0 en Subnormal subgroup Abelian normal subgroup 0 en Abelian normal subgroup Abelian group 0 en Abelian group Simple group 0 en Simple group Dedekind group 0 en Dedekind group Normalizer of a subgroup 0 en Normalizer of a subgroup Characteristic subgroup 0 en Characteristic subgroup Fully invariant subgroup 0 en Fully invariant subgroup Abelian normal subgroup 0 en Abelian normal subgroup Hall-relatively weakly closed subgroup 0 en Hall-relatively weakly closed subgroup Sylow-relatively weakly closed subgroup 0 en Sylow-relatively weakly closed subgroup Isomorph-normal subgroup 0 en Isomorph-normal subgroup Isomorph-normal characteristic subgroup 0 en Isomorph-normal characteristic subgroup Maximal subgroup of finite nilpotent group 0 en Maximal subgroup of finite nilpotent group Isomorph-normal coprime automorphism-invariant subgroup 0 en Isomorph-normal coprime automorphism-invariant subgroup Subnormal subgroup 0 en Subnormal subgroup 0 Fourth isomorphism theorem#Normal subgroup# b832a31b455a432a186dad58c6c8b94c 0 Normality is strongly intersection-closed#Normal subgroup;1# 1e1e4dfa0b004602c838399108acb341 0 Normality is strongly intersection-closed#Normal subgroup# b832a31b455a432a186dad58c6c8b94c 0 Characteristic implies normal#Normal subgroup;1# 1e1e4dfa0b004602c838399108acb341 0 Normality is strongly join-closed#Normal subgroup# b832a31b455a432a186dad58c6c8b94c 0 Normal not implies characteristic#Normal subgroup;1# 1e1e4dfa0b004602c838399108acb341 0 First isomorphism theorem#Normal subgroup# b832a31b455a432a186dad58c6c8b94c 0 Second isomorphism theorem#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Normality is not transitive#Normal subgroup;1# 1e1e4dfa0b004602c838399108acb341 0 Third isomorphism theorem#Normal subgroup# b832a31b455a432a186dad58c6c8b94c 0 Normal subgroup equals kernel of homomorphism#Normal subgroup;1# 1e1e4dfa0b004602c838399108acb341 0 Normal subgroup equals kernel of homomorphism#Normal subgroup# b832a31b455a432a186dad58c6c8b94c 0 Characteristic of normal implies normal#Normal subgroup# b832a31b455a432a186dad58c6c8b94c 0 Characteristic of normal implies normal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Left transiter of normal is characteristic#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Intermediately automorph-conjugate of normal implies weakly pronormal#Normal subgroup# b832a31b455a432a186dad58c6c8b94c 0 Normal and self-centralizing implies coprime automorphism-faithful#Normal subgroup# b832a31b455a432a186dad58c6c8b94c 0 Central implies normal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Central factor implies normal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Direct factor implies normal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Normal implies permutable#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Normal implies permutable#Normal subgroup# b832a31b455a432a186dad58c6c8b94c 0 Nilpotent implies every maximal subgroup is normal#Normal subgroup# b832a31b455a432a186dad58c6c8b94c 0 Normal and self-centralizing implies normality-large#Normal subgroup# b832a31b455a432a186dad58c6c8b94c 0 Commutator of a normal subgroup and a subset implies 2-subnormal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Commutator of a group and a subgroup implies normal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Normal not implies strongly potentially characteristic#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Left-transitively WNSCDIN not implies normal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Permutable not implies normal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Subnormal not implies normal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Quotient group need not be isomorphic to any subgroup#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Normal not implies amalgam-characteristic#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Normal not implies potentially verbal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Index three implies normal or double coset index two#Normal subgroup# b832a31b455a432a186dad58c6c8b94c 0 Normal implies join-transitively subnormal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Normal not implies normal-potentially characteristic#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Normal not implies central factor#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Normal not implies potentially fully invariant#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Proper and normal in quasisimple implies central#Normal subgroup# b832a31b455a432a186dad58c6c8b94c 0 Normal not implies image-potentially fully invariant#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Conjugate-comparable not implies normal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Normal implies modular#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Normal-extensible not implies normal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Normal not implies left-transitively fixed-depth subnormal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Normal not implies right-transitively fixed-depth subnormal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Normal not implies direct factor#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Normal not implies normal-potentially relatively characteristic#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Intermediately isomorph-conjugate of normal implies pronormal#Normal subgroup# b832a31b455a432a186dad58c6c8b94c 0 Potentially verbal implies normal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac 0 Subgroup of index two is normal#Normal subgroup;2# 5fc29bfd103738ece3dc328ddef969ac Ubiquity of normality 0 en Ubiquity of normality Satisfies property 132 en Satisfies property Proves property satisfaction of 132 en Proves property satisfaction of Analogue of 132 en Analogue of Conjunction involving 132 en Conjunction involving Uses property satisfaction of 132 en Uses property satisfaction of Operator related to 132 en Operator related to Defining ingredient 132 en Defining ingredient Stronger than 132 en Stronger than Weaker than 132 en Weaker than Page 132 en Page Survey article about 132 en Survey article about