]> 2026-07-04T12:46:18+00:00 Fully invariant subgroup 0 en 2 Term invariant under all endomorphisms endomorphism-invariant 2021-08-18T15:35:01Z 2459445.1493171 Fully invariant subgroup 0 Fully invariant subgroup#Levi33 0 Fully invariant subgroup#Baer44 0 Fully invariant subgroup#RobinsonGT 0 Fully invariant subgroup#Levi33 0 Fully invariant subgroup#Baer44 0 1 table 2 [[Defining ingredient::Fully invariant subgroup]] Fully invariant subgroup# QUERYb7e6aec09ae9f9925480125dca67fd8c 0 2 table 5 [[Fact about:: <q>[[Page::Fully invariant subgroup]] [[Number::1]]</q> ]] Fully invariant subgroup# QUERYa8ef0836ed61842b006a1167a8867541 0 2 table 3 [[Fact about.Page::Fully invariant subgroup]] Fully invariant subgroup# QUERY5bca466c39f413c5aa2b83238bac8cb0 0 1 table 2 [[Survey article about::Fully invariant subgroup]] Fully invariant subgroup# QUERYf7b1702af91fd767ac39730fbd60ad26 0 2 plainlist 3 [[Survey article about.Defining ingredient::Fully invariant subgroup]] Fully invariant subgroup# QUERY573831f6007de1fa7b57317f6e1ca50c 0 1 plainlist 2 [[Analogue of::Fully invariant subgroup]] Fully invariant subgroup# QUERYdfdd7769877e9b7209ae8ea62243e304 0 1 plainlist 2 [[Variation of::Fully invariant subgroup]] Fully invariant subgroup# QUERY03fbd84e47d12bc2735f0d1e83aadd22 0 1 plainlist 2 [[Opposite of::Fully invariant subgroup]] Fully invariant subgroup# QUERYabb6f96db344a62f367803f3e3d7f834 0 2 plainlist 4 [[Fact about.Page::Fully invariant subgroup]] [[Category:Subgroup property implications]] Fully invariant subgroup# QUERY3fd38224645747ffb747f7e3f73b760d 0 2 plainlist 4 [[Fact about.Page::Fully invariant subgroup]] [[Category:Subgroup property non-implications]] Fully invariant subgroup# QUERY1d72d10ae90ff1c7a9adf8651fa56954 0 2 plainlist 4 [[Fact about.Page::Fully invariant subgroup]] [[Category:Subgroup metaproperty satisfactions]] Fully invariant subgroup# QUERYbba456b68fa51ca95a2231f24f623a46 0 2 plainlist 4 [[Fact about.Page::Fully invariant subgroup]] [[Category:Subgroup metaproperty dissatisfactions]] Fully invariant subgroup# QUERY0f02c0ada05ed7f74371325916bcf191 0 2 plainlist 4 [[Fact about.Page::Fully invariant subgroup]] [[Category:Subgroup property satisfactions]] [[Category:Subgroup property satisfactions]] [[Fact about.Page::Fully invariant subgroup]] Fully invariant subgroup# QUERY31e9fddeaedd459ed069379bafd93dcd 0 2 plainlist 4 [[Fact about.Page::Fully invariant subgroup]] [[Category:Subgroup property dissatisfactions]] [[Category:Subgroup property dissatisfactions]] [[Fact about.Page::Fully invariant subgroup]] Fully invariant subgroup# QUERY0d9a1533d9a961951971ce37702a57a0 0 1 table 2 [[Uses property satisfaction of::Fully invariant subgroup]] Fully invariant subgroup# QUERY214e53ed4a6ebd3c13d1e2a5a4b68bc0 0 1 table 2 [[Proves property satisfaction of::Fully invariant subgroup]] Fully invariant subgroup# QUERY7ba17010e97a7ea8193c369f2fd9b6ba 0 1 table 2 [[Variation of::Characteristicity]] Fully invariant subgroup# QUERYf9b3e909347f62b44108b19c5b43c47b 0 2 table 6 <q> <q>[[Satisfies property::Fully invariant subgroup]]</q> OR [[Satisfies property.Stronger than::Fully invariant subgroup]] [[Category:Particular subgroups]]</q> Fully invariant subgroup# QUERY8f6e99ff692b3074e32fd9271dfdbfc5 0 2 table 6 <q> <q>[[Dissatisfies property::Fully invariant subgroup]]</q> OR [[Dissatisfies property.Weaker than::Fully invariant subgroup]] [[Category:Particular subgroups]]</q> Fully invariant subgroup# QUERY0563a542b7d521fc77987631852d30a6 0 2 table 12 <q>[[Satisfies property::Fully invariant subgroup]] [[Dissatisfies property::Verbal subgroup]] [[Category:Particular subgroups]] OR [[Satisfies property.Stronger than::Fully invariant subgroup]] [[Dissatisfies property.Weaker than::Verbal subgroup]] [[Category:Particular subgroups]]</q> Fully invariant subgroup# QUERYafb38eca7f87faf3c817d0f5ed6be9be 0 1 list 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Verbal subgroup]] Fully invariant subgroup# QUERYf0597546967e4d86ab32de664ed04b79 0 1 broadtable 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Verbal subgroup]] Fully invariant subgroup# QUERY9b84dcfe8df747287cbbe68217318024 0 1 list 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Existentially bound-word subgroup]] Fully invariant subgroup# QUERY053da978c3153153e0f90afad7838ca2 0 1 broadtable 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Existentially bound-word subgroup]] Fully invariant subgroup# QUERYb94950d031b682f863d963f37c8f449f 0 1 list 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Homomorph-containing subgroup]] Fully invariant subgroup# QUERY577048873472b02a8d7fc390d490dac6 0 1 broadtable 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Homomorph-containing subgroup]] Fully invariant subgroup# QUERY49f2a41707cbe813a2346efa088c5ae6 0 1 list 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Subhomomorph-containing subgroup]] Fully invariant subgroup# QUERY23c0a97746ab83bfcb401b8e6a3f0630 0 1 broadtable 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Subhomomorph-containing subgroup]] Fully invariant subgroup# QUERYaf6e97ae4053231e5d82b44ea8bd043c 0 1 list 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Order-containing subgroup]] Fully invariant subgroup# QUERY0175ba57879daf4f0557d1ec59f3b4ca 0 1 broadtable 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Order-containing subgroup]] Fully invariant subgroup# QUERY18ceded66cb3e75c7058eceed2bd30fe 0 1 list 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Variety-containing subgroup]] Fully invariant subgroup# QUERYd3190681852de694264b2bc705acac40 0 1 broadtable 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Variety-containing subgroup]] Fully invariant subgroup# QUERY93d59397d27268647a6bb507e43cd54a 0 1 list 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Normal subgroup having no nontrivial homomorphism to its quotient group]] Fully invariant subgroup# QUERYfc72aaa1b9079a62ab4088c60b01274a 0 1 broadtable 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Normal subgroup having no nontrivial homomorphism to its quotient group]] Fully invariant subgroup# QUERY149ff7e1b5000e54b1b146f0bfb09b76 0 1 list 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Normal Hall subgroup]] Fully invariant subgroup# QUERY896b85c224a2cda78f260a317a2917c5 0 1 broadtable 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Normal Hall subgroup]] Fully invariant subgroup# QUERY65dfb5dcb6e50f0cc6ddba9a21c942b2 0 1 list 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Normal Sylow subgroup]] Fully invariant subgroup# QUERY9f05829f5f614ddbfce520fcf306c8ff 0 1 broadtable 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Normal Sylow subgroup]] Fully invariant subgroup# QUERY522253b3e04d60fea9e4fdbab46bf3cd 0 1 list 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Quotient-subisomorph-containing subgroup]] Fully invariant subgroup# QUERY5c15e42c313b1b51652fa996de714f99 0 1 broadtable 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Quotient-subisomorph-containing subgroup]] Fully invariant subgroup# QUERYcc8e3dfbc0b25e4d1f577496f1aa5e82 0 1 list 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Image-closed fully invariant subgroup]] Fully invariant subgroup# QUERY658c6d6cc0f688c268f1e769f703f6f1 0 1 broadtable 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Image-closed fully invariant subgroup]] Fully invariant subgroup# QUERY1c579e5714a6703f06628df953209e96 0 1 list 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Intermediately fully invariant subgroup]] Fully invariant subgroup# QUERY090de556f08cebe39c9ce24933edb645 0 1 broadtable 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Intermediately fully invariant subgroup]] Fully invariant subgroup# QUERYdc7f18d9557331a19521b915152d01ba 0 1 list 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Transfer-closed fully invariant subgroup]] Fully invariant subgroup# QUERY9f040dd827cd98883436e787dec53e2e 0 1 broadtable 4 [[Stronger than::Fully invariant subgroup]] [[Weaker than::Transfer-closed fully invariant subgroup]] Fully invariant subgroup# QUERY68bc5cd47e410ce8c7d5c3e7aff68066 0 2 table 12 <q>[[Satisfies property::Characteristic subgroup]] [[Dissatisfies property::Fully invariant subgroup]] [[Category:Particular subgroups]] OR [[Satisfies property.Stronger than::Characteristic subgroup]] [[Dissatisfies property.Weaker than::Fully invariant subgroup]] [[Category:Particular subgroups]]</q> Fully invariant subgroup# QUERY289079cacd555bbe0c2c7ddb759e58f2 0 1 list 4 [[Stronger than::Characteristic subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERY706af4aeca70c5b52f9d6f213b4c761b 0 1 broadtable 4 [[Stronger than::Characteristic subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERY98d1861686ad2da1a3e9803e73541e0b 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERY1ddef1eb011c223f2dd6d21c556259a8 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERY46b5b4b694ca950e466e8311ac33685a 0 1 list 4 [[Stronger than::Strictly characteristic subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERYcf03a15f0c06a8d2fb2b1388a660caf5 0 1 broadtable 4 [[Stronger than::Strictly characteristic subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERY1432faec0cac6c11255abe1a232b469e 0 1 list 4 [[Stronger than::Injective endomorphism-invariant subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERYa0684f34107ab9e45fc63c2b444c68e8 0 1 broadtable 4 [[Stronger than::Injective endomorphism-invariant subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERY4432328abbbbe15c985ab02519987bd4 0 1 list 4 [[Stronger than::Retraction-invariant subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERYbc2b14db35515b059a5ed6a4ab286769 0 1 broadtable 4 [[Stronger than::Retraction-invariant subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERY0d5388a93492e094107ba210f532ea58 0 1 list 4 [[Stronger than::Endomorph-dominating subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERYe98dabac0143fcd0636e40d14b6e33df 0 1 broadtable 4 [[Stronger than::Endomorph-dominating subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERY0720607dd213d880a6dfaf9466a2ff79 0 1 list 4 [[Stronger than::Potentially fully invariant subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERY6988cdd134e054af4f548f5cb8918a9f 0 1 broadtable 4 [[Stronger than::Potentially fully invariant subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERY09f4053df36d71aa6729df85c49953ad 0 1 list 4 [[Stronger than::Finite direct power-closed characteristic subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERY47b7d416452cbf3355a5390a2e68a59d 0 1 broadtable 4 [[Stronger than::Finite direct power-closed characteristic subgroup]] [[Weaker than::Fully invariant subgroup]] Fully invariant subgroup# QUERYa76e58c81692bf2b6d529783f4c64788 0 1 plainlist 2 [[Satisfies metaproperty::Second-order subgroup property]] Fully invariant subgroup# QUERYe7955396f5bf66153df1ba4f6eab9191 0 1 plainlist 2 [[Satisfies metaproperty::Function restriction-expressible subgroup property]] Fully invariant subgroup# QUERY6aa24c02f8e67de24223fa849790e0e6 0 1 plainlist 2 [[Satisfies metaproperty::GAP-testable subgroup property]] Fully invariant subgroup# QUERYab3deb33606903472662717bd3ca61c2 0 1 plainlist 2 [[Satisfies metaproperty::GAP-listable subgroup property]] Fully invariant subgroup# QUERYe6c7e410aa0a9124a787ec94e3720a50 0 1 plainlist 2 [[Satisfies metaproperty::GAP-codable subgroup property]] Fully invariant subgroup# QUERY0db1d57349eaa4fa10fe190d719c5331 0 2 table 7 <q>[[Category:Particular subgroups]] [[Satisfies property::Fully invariant subgroup]] OR [[Category:Particular subgroups]] [[Satisfies property.Stronger than::Fully invariant subgroup]]</q> Fully invariant subgroup# QUERYe20887227b90dbea5bc175029cc478e3 0 2 table 7 <q>[[Category:Particular subgroups]] [[Dissatisfies property::Fully invariant subgroup]] OR [[Category:Particular subgroups]] [[Dissatisfies property.Weaker than::Fully invariant subgroup]]</q> Fully invariant subgroup# QUERY14dbb980ee6e606de42aa170b56cb927 Center 0 en Center Derived subgroup 0 en Derived subgroup Center of dihedral group:D8 0 en Center of dihedral group:D8 Verbal implies fully invariant 0 en Verbal implies fully invariant Fully invariant implies characteristic 0 en Fully invariant implies characteristic Fully invariant of strictly characteristic implies strictly characteristic 0 en Fully invariant of strictly characteristic implies strictly characteristic Fully invariant implies finite direct power-closed characteristic 0 en Fully invariant implies finite direct power-closed characteristic Direct factor of fully invariant subgroup 0 en Direct factor of fully invariant subgroup Normal subgroup 0 en Normal subgroup Characteristic subgroup 0 en Characteristic subgroup Direct factor of fully invariant subgroup 0 en Direct factor of fully invariant subgroup 0 Fully invariant implies characteristic#Fully invariant subgroup;2# a90e337ebfc2cd15edebf6245b5a345f 0 Verbal implies fully invariant#Fully invariant subgroup;2# a90e337ebfc2cd15edebf6245b5a345f 0 Fully invariant of strictly characteristic implies strictly characteristic#Fully invariant subgroup# c5eaaf843cb45894c9e3383e53884742 0 Fully invariant of strictly characteristic implies strictly characteristic#Fully invariant subgroup;2# a90e337ebfc2cd15edebf6245b5a345f 0 Strictly characteristic not implies fully invariant#Fully invariant subgroup;2# a90e337ebfc2cd15edebf6245b5a345f 0 Characteristic not implies potentially fully invariant#Fully invariant subgroup;3# 9d32d3012e31ef7ae0e1e9b1c3511911 0 Characteristic not implies fully invariant#Fully invariant subgroup;1# 448f8b07ebdd171cac9216d02429a98c 0 Image-closed characteristic not implies fully invariant#Fully invariant subgroup;2# a90e337ebfc2cd15edebf6245b5a345f 0 Finite direct power-closed characteristic not implies fully invariant#Fully invariant subgroup;2# a90e337ebfc2cd15edebf6245b5a345f 0 Fully invariant subgroup of abelian group not implies divisibility-closed#Fully invariant subgroup;2# a90e337ebfc2cd15edebf6245b5a345f 0 Characteristic direct factor not implies fully invariant#Fully invariant subgroup;2# a90e337ebfc2cd15edebf6245b5a345f 0 Fully invariant implies finite direct power-closed characteristic#Fully invariant subgroup;2# a90e337ebfc2cd15edebf6245b5a345f Dissatisfies property 132 en Dissatisfies property Satisfies property 132 en Satisfies property Proves property satisfaction of 132 en Proves property satisfaction of Uses property satisfaction of 132 en Uses property satisfaction of Defining ingredient 132 en Defining ingredient Weaker than 132 en Weaker than Page 132 en Page