]> 2026-09-07T07:03:11+00:00 Abelian normal subgroup 0 en Term 2013-08-12T20:40:54Z 2456517.3617361 Abelian normal subgroup 0 1 table 2 [[Defining ingredient::Abelian normal subgroup]] Abelian normal subgroup# QUERY9a22aaeb3ff9157f1785f67f592029bc 0 2 table 5 [[Fact about:: <q>[[Page::Abelian normal subgroup]] [[Number::1]]</q> ]] Abelian normal subgroup# QUERY64dd1601dfa4577a2bf41dd3b25e5055 0 2 table 3 [[Fact about.Page::Abelian normal subgroup]] Abelian normal subgroup# QUERYab27bbd2e5bd81792b7679cf0110dc67 0 1 table 2 [[Survey article about::Abelian normal subgroup]] Abelian normal subgroup# QUERY21924b74624faa08a294e156b6f673e8 0 2 plainlist 3 [[Survey article about.Defining ingredient::Abelian normal subgroup]] Abelian normal subgroup# QUERY7f22a1d7b91867a12196e31a5263e4c4 0 1 plainlist 2 [[Analogue of::Abelian normal subgroup]] Abelian normal subgroup# QUERY847e5123c3ff4b324b7d757ca039d1b2 0 1 plainlist 2 [[Variation of::Abelian normal subgroup]] Abelian normal subgroup# QUERY91814833e1aef716fbf68eb788a805c7 0 1 plainlist 2 [[Opposite of::Abelian normal subgroup]] Abelian normal subgroup# QUERY00a9f7bce9b79d399e4b182f347afa31 0 2 plainlist 4 [[Fact about.Page::Abelian normal subgroup]] [[Category:Subgroup property implications]] Abelian normal subgroup# QUERY50423977b3fb4d84124f60ada6fdb635 0 2 plainlist 4 [[Fact about.Page::Abelian normal subgroup]] [[Category:Subgroup property non-implications]] Abelian normal subgroup# QUERY86ff493626fa22d1e26e339a05f7f8da 0 2 plainlist 4 [[Fact about.Page::Abelian normal subgroup]] [[Category:Subgroup metaproperty satisfactions]] Abelian normal subgroup# QUERY2f1f16a35ce83cc569c393a241ef6447 0 2 plainlist 4 [[Fact about.Page::Abelian normal subgroup]] [[Category:Subgroup metaproperty dissatisfactions]] Abelian normal subgroup# QUERYe1bf9b91d2c7f4ae55a0ba8b7f3d9cde 0 2 plainlist 4 [[Fact about.Page::Abelian normal subgroup]] [[Category:Subgroup property satisfactions]] [[Category:Subgroup property satisfactions]] [[Fact about.Page::Abelian normal subgroup]] Abelian normal subgroup# QUERY69a4788276061b428e86e2d72464ac25 0 2 plainlist 4 [[Fact about.Page::Abelian normal subgroup]] [[Category:Subgroup property dissatisfactions]] [[Category:Subgroup property dissatisfactions]] [[Fact about.Page::Abelian normal subgroup]] Abelian normal subgroup# QUERYa4e1a83eb142ee729bc0a3d3b291fc87 0 1 table 2 [[Uses property satisfaction of::Abelian normal subgroup]] Abelian normal subgroup# QUERYe8934b81f7cc161723413f24d505a774 0 1 table 2 [[Proves property satisfaction of::Abelian normal subgroup]] Abelian normal subgroup# QUERY217f45bd714acd95eca8cc6c85f9dcd3 0 2 table 5 [[Satisfies property::Normal subgroup]] [[Subgroup part.Satisfies property::Abelian group]] Abelian normal subgroup# QUERYdd03ba5361becc5abc67af060b2a33ca 0 1 table 2 [[Dissatisfies property::Normal subgroup]] Abelian normal subgroup# QUERY3f56e023ec6d443da87c702e3f7640ad 0 2 table 3 [[Subgroup part.Dissatisfies property::Abelian group]] Abelian normal subgroup# QUERY39d400ec0825876a772a2700dc628dc7 0 3 table 36 <q>[[Satisfies property::Normal subgroup]] [[Subgroup part.Satisfies property::Abelian group]] [[Group part.Importance rank::1]] OR [[Satisfies property.Stronger than::Normal subgroup]] [[Subgroup part.Satisfies property::Abelian group]] [[Group part.Importance rank::1]] OR [[Satisfies property::Normal subgroup]] [[Subgroup part.Satisfies property.Stronger than::Abelian group]] [[Group part.Importance rank::1]] OR [[Satisfies property.Stronger than::Normal subgroup]] [[Subgroup part.Satisfies property.Stronger than::Abelian group]] [[Group part.Importance rank::1]]</q> Abelian normal subgroup# QUERY384fe84cc65a9383bcf6bf5125f8e633 0 3 table 36 <q>[[Satisfies property::Normal subgroup]] [[Subgroup part.Satisfies property::Abelian group]] [[Group part.Importance rank::2]] OR [[Satisfies property.Stronger than::Normal subgroup]] [[Subgroup part.Satisfies property::Abelian group]] [[Group part.Importance rank::2]] OR [[Satisfies property::Normal subgroup]] [[Subgroup part.Satisfies property.Stronger than::Abelian group]] [[Group part.Importance rank::2]] OR [[Satisfies property.Stronger than::Normal subgroup]] [[Subgroup part.Satisfies property.Stronger than::Abelian group]] [[Group part.Importance rank::2]]</q> Abelian normal subgroup# QUERY50840783233556594a59eff5a81184f7 0 3 table 36 <q>[[Satisfies property::Normal subgroup]] [[Subgroup part.Satisfies property::Abelian group]] [[Group part.Importance rank::3]] OR [[Satisfies property.Stronger than::Normal subgroup]] [[Subgroup part.Satisfies property::Abelian group]] [[Group part.Importance rank::3]] OR [[Satisfies property::Normal subgroup]] [[Subgroup part.Satisfies property.Stronger than::Abelian group]] [[Group part.Importance rank::3]] OR [[Satisfies property.Stronger than::Normal subgroup]] [[Subgroup part.Satisfies property.Stronger than::Abelian group]] [[Group part.Importance rank::3]]</q> Abelian normal subgroup# QUERYe6efe18a68a04ef0549f5d57a95149c2 0 1 list 4 [[Stronger than::Abelian normal subgroup]] [[Weaker than::Abelian direct factor]] Abelian normal subgroup# QUERY6e05077cd14fa181e41507c842e906f3 0 1 broadtable 4 [[Stronger than::Abelian normal subgroup]] [[Weaker than::Abelian direct factor]] Abelian normal subgroup# QUERY54c8e9434599fb4dd7932ef65a91bcd8 0 1 list 4 [[Stronger than::Abelian normal subgroup]] [[Weaker than::Central subgroup]] Abelian normal subgroup# QUERY048ebcaaa7ec8f72d848abc2a37f99ea 0 1 broadtable 4 [[Stronger than::Abelian normal subgroup]] [[Weaker than::Central subgroup]] Abelian normal subgroup# QUERYa2045f7f5db630888a4387172304f8f4 0 1 list 4 [[Stronger than::Abelian normal subgroup]] [[Weaker than::Cyclic normal subgroup]] Abelian normal subgroup# QUERYb8ba068bf4b080f14e23e0b9d8bb0d69 0 1 broadtable 4 [[Stronger than::Abelian normal subgroup]] [[Weaker than::Cyclic normal subgroup]] Abelian normal subgroup# QUERY0e48774b1964bc4c41598bc918627430 0 1 list 4 [[Stronger than::Abelian normal subgroup]] [[Weaker than::Abelian characteristic subgroup]] Abelian normal subgroup# QUERYa2e4ee36720bedbc1044ce582a4fbb56 0 1 broadtable 4 [[Stronger than::Abelian normal subgroup]] [[Weaker than::Abelian characteristic subgroup]] Abelian normal subgroup# QUERY42c29cccf9b7691dcf20e56c77a971f2 0 1 list 4 [[Stronger than::Abelian normal subgroup]] [[Weaker than::Elementary abelian normal subgroup]] Abelian normal subgroup# QUERYa5df2843bc61ff7d61d022dcafcf1860 0 1 broadtable 4 [[Stronger than::Abelian normal subgroup]] [[Weaker than::Elementary abelian normal subgroup]] Abelian normal subgroup# QUERYc6fa5a68144c59aec6a2731775ac628b 0 1 list 4 [[Stronger than::Abelian normal subgroup]] [[Weaker than::Maximal among abelian normal subgroups]] Abelian normal subgroup# QUERYba2249ac5b6d480d0cf669f1c484ca66 0 1 broadtable 4 [[Stronger than::Abelian normal subgroup]] [[Weaker than::Maximal among abelian normal subgroups]] Abelian normal subgroup# QUERY3a9fcf1f2883df638b33b9d4c612f53d 0 1 list 4 [[Stronger than::Abelian normal subgroup]] [[Weaker than::Maximal among abelian characteristic subgroups]] Abelian normal subgroup# QUERYa2859e9b3bb552aafc17f6363eb9fd24 0 1 broadtable 4 [[Stronger than::Abelian normal subgroup]] [[Weaker than::Maximal among abelian characteristic subgroups]] Abelian normal subgroup# QUERY4158cd1227e0553f315d54def6209ef3 0 1 list 4 [[Stronger than::Commutator-in-center subgroup]] [[Weaker than::Abelian normal subgroup]] Abelian normal subgroup# QUERY96027380a65d7e666552137ad35295f4 0 1 broadtable 4 [[Stronger than::Commutator-in-center subgroup]] [[Weaker than::Abelian normal subgroup]] Abelian normal subgroup# QUERY5b4d3e6832f2acd796bc97dd9d9a3ce8 0 1 list 4 [[Stronger than::Dedekind normal subgroup]] [[Weaker than::Abelian normal subgroup]] Abelian normal subgroup# QUERY4fcf7877c9f9dbd8c6c3a9bfafeb6902 0 1 broadtable 4 [[Stronger than::Dedekind normal subgroup]] [[Weaker than::Abelian normal subgroup]] Abelian normal subgroup# QUERY26814257a35168b91ae845a96d22fa5c 0 1 list 4 [[Stronger than::Class two normal subgroup]] [[Weaker than::Abelian normal subgroup]] Abelian normal subgroup# QUERYddc5f371aeb1e96c741451d3e3db8def 0 1 broadtable 4 [[Stronger than::Class two normal subgroup]] [[Weaker than::Abelian normal subgroup]] Abelian normal subgroup# QUERY32c06593924e0454fd1fc80c1d9ed6d0 0 1 list 4 [[Stronger than::Nilpotent normal subgroup]] [[Weaker than::Abelian normal subgroup]] Abelian normal subgroup# QUERYde31af6fb29d4d2b79513033edee91b0 0 1 broadtable 4 [[Stronger than::Nilpotent normal subgroup]] [[Weaker than::Abelian normal subgroup]] Abelian normal subgroup# QUERYaa51112f191032b82b139028d689885b 0 1 list 4 [[Stronger than::Solvable normal subgroup]] [[Weaker than::Abelian normal subgroup]] Abelian normal subgroup# QUERYbe3b8dd69f2c61f87aac4d9490d2664d 0 1 broadtable 4 [[Stronger than::Solvable normal subgroup]] [[Weaker than::Abelian normal subgroup]] Abelian normal subgroup# QUERYa65da5f7b1ea99a2ad12988cbe943067 0 1 list 4 [[Stronger than::Normal subgroup]] [[Weaker than::Abelian normal subgroup]] Abelian normal subgroup# QUERYa8da33c55c329912413a1a153f48e786 0 1 broadtable 4 [[Stronger than::Normal subgroup]] [[Weaker than::Abelian normal subgroup]] Abelian normal subgroup# QUERY29a0ad8e6dad7747a71d8cb316f00545 0 1 table 4 [[Variation of::Abelian normal subgroup]] [[Satisfies metaproperty::Transitive subgroup property]] Abelian normal subgroup# QUERYab64854d016f0081b2e56186ef1ad452 0 1 table 4 [[Variation of::Abelian normal subgroup]] [[Dissatisfies metaproperty::Transitive subgroup property]] Abelian normal subgroup# QUERY5bc81d8cc81d2ff048855aa072d470a1 0 1 table 2 [[Dissatisfies metaproperty::Transitive subgroup property]] Abelian normal subgroup# QUERY70919a9a3e5b8798c63d34ecbaf2e1c5 0 2 table 3 [[Fact about.Page::Transitive subgroup property]] Abelian normal subgroup# QUERYe34b52d523c639aefb82d361d1eec897 0 1 plainlist 4 [[Variation of::Abelian normal subgroup]] [[Satisfies metaproperty::Intermediate subgroup condition]] Abelian normal subgroup# QUERY264434f8fca278444a1d9998add3a4a8 0 1 plainlist 4 [[Variation of::Abelian normal subgroup]] [[Dissatisfies metaproperty::Intermediate subgroup condition]] Abelian normal subgroup# QUERY7a5f0c6474b8a69332f99a77f051e6d7 0 1 plainlist 2 [[Satisfies metaproperty::Intermediate subgroup condition]] Abelian normal subgroup# QUERY9d7932892c4bf52873c53226e9013449 0 2 plainlist 3 [[Fact about.Page::Intermediate subgroup condition]] Abelian normal subgroup# QUERYbab61f493e5e2c47de7504662d46be45 0 1 plainlist 2 [[Satisfies metaproperty::Image condition]] Abelian normal subgroup# QUERYebc0a3722a918abd76636ee436900d35 0 1 plainlist 4 [[Variation of::Abelian normal subgroup]] [[Satisfies metaproperty::Intersection-closed subgroup property]] Abelian normal subgroup# QUERYc7c59552c09d8ef509c1aa338c5f8706 0 1 plainlist 4 [[Variation of::Abelian normal subgroup]] [[Dissatisfies metaproperty::Intersection-closed subgroup property]] Abelian normal subgroup# QUERY456a3e9ff3f265b57649a6872e9add35 0 1 plainlist 2 [[Satisfies metaproperty::Intersection-closed subgroup property]] Abelian normal subgroup# QUERY993e49e16d937d6a57d58b34bed96ad4 0 1 plainlist 2 [[Satisfies metaproperty::Strongly intersection-closed subgroup property]] Abelian normal subgroup# QUERY1fe326dd858d414ec146df7839d1c85e 0 1 plainlist 2 [[Dissatisfies metaproperty::Intersection-closed subgroup property]] Abelian normal subgroup# QUERYb336525f07412f93228f645d13c3a41e Central implies abelian normal 0 en Central implies abelian normal 2-Engel group 0 en 2-Engel group Maximal among abelian characteristic subgroups 0 en Maximal among abelian characteristic subgroups Abelian characteristic subgroup 0 en Abelian characteristic subgroup Normal subgroup 0 en Normal subgroup 0 Degree of irreducible representation divides index of abelian normal subgroup#Abelian normal subgroup;1# b1fa5587dafdec308c8467ae4eb78d31 0 Degree of irreducible representation divides index of abelian normal subgroup#Abelian normal subgroup# 329ee09bcdf7859ac7bb1cdec935e3d2 0 P-constrained and p-stable implies abelian normal subgroup of Sylow subgroup is contained in (p',p)-core#Abelian normal subgroup# 329ee09bcdf7859ac7bb1cdec935e3d2 0 Central implies abelian normal#Abelian normal subgroup;2# b853d2f4a41263224c25c3ebc3d5c64a 0 Abelian normal not implies central#Abelian normal subgroup;2# b853d2f4a41263224c25c3ebc3d5c64a 0 Series-equivalent abelian-quotient abelian not implies automorphic#Abelian normal subgroup;2# b853d2f4a41263224c25c3ebc3d5c64a Proves property satisfaction of 132 en Proves property satisfaction of Defining ingredient 132 en Defining ingredient Stronger than 132 en Stronger than Weaker than 132 en Weaker than Page 132 en Page