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The query [[Defining ingredient::Normal subgroup]] was answered by the SMWSQLStore3 in 0.0050 seconds.


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 Quick phraseDefining ingredient
2-subnormal subgroupNormal subgroup
Normal closure
Normalizer of a subgroup
Conjugate subgroups
Normal core of normalizer
Normal core
Subnormal subgroup
Subnormal depth
Commutator of two subgroups
3-subnormal subgroupNormal subgroup
2-subnormal subgroup
4-subnormal subgroupSubnormal subgroup
Subnormal depth
2-subnormal subgroup
Normal subgroup
3-subnormal subgroup
Abelian groupCenter
Derived subgroup
Normal subgroup
Diagonal-in-square operator
Abelian normal subgroupNormal subgroup
Abelian group
Abelian normal subgroup of maximum rankAbelian normal subgroup
Abelian group
Normal subgroup
Rank of a p-group
Normal rank of a p-group
Almost normal subgroupNormal subgroup
Subgroup of finite index
Normalizer of a subgroup
Index of a subgroup
Conjugate subgroups
Almost subnormal subgroupNormal subgroup
Subgroup of finite index
Automorph-conjugate subgroupAutomorphic subgroups
Conjugate subgroups
Normal subgroup
Normalizer of a subgroup
Automorphism-faithful normal subgroupAutomorphism-faithful subgroup
Normal subgroup
C-closed normal subgroupC-closed subgroup
Normal subgroup
Central factorfactor in central product
product with centralizer is whole group
quotient action by outer automorphisms is trivial
every inner automorphism restricts to an inner automorphism
Inner automorphism
Centralizer
Normal subgroup
Quotient group maps to outer automorphism group of normal subgroup
Internal central product
Image-potentially operator
Direct factor
Upper join-closure operator
Cocentral subgroup
Central factor of normal subgroupCentral factor
Normal subgroup
Normal closure
Centralizer-free normal subgroupCentralizer-free subgroup
Normal subgroup
Class two normal subgroupNormal subgroup
Group of nilpotency class two
Closed normal subgroupClosed subgroup of semitopological group
Normal subgroup
Commutator of a normal subgroup and a subsetNormal subgroup
Commutator of two subsets
Commutator
Commutator-in-center subgroupNormal subgroup
Commutator-in-centralizer subgroup
Complete direct factorDirect factor
Complete group
Normal subgroup
Complemented normal subgroup
Complete groupNormal subgroup
Direct factor
Completely divisibility-closed normal subgroupCompletely divisibility-closed subgroup
Normal subgroup
Conjugacy-closed normal subgroupConjugacy-closed subgroup
Normal subgroup
Coprime automorphism-faithful normal subgroupCoprime automorphism-faithful subgroup
Normal subgroup
Coprime automorphism-invariant normal subgroupCoprime automorphism-invariant subgroup
Normal subgroup
Coprime automorphism-invariant normal subgroup of group of prime power orderCoprime automorphism-invariant normal subgroup
Group of prime power order
Normal subgroup
Normal subgroup of group of prime power order
Coprime automorphism-invariant subgroup
Coprime automorphism-invariant subgroup of group of prime power order
Cyclic normal subgroupNormal subgroup
Cyclic group
Dedekind groupevery subgroup is normal
every cyclic subgroup is normal
normal closure of element is cyclic
Normal subgroup
Inner automorphism
Power automorphism
Normal closure
Levi operator
Cyclic group
Hamiltonian operator
Dedekind normal subgroupNormal subgroup
Dedekind group
Direct factorfactor in internal direct product
normal with normal complement
has centralizing complement
Internal direct product
Normal subgroup
Normal complement
Retract
Direct factor of normal subgroupDirect factor
Normal subgroup
Normal closure
Divisible normal subgroupNormal subgroup
Divisible group
Elementary abelian normal subgroupNormal subgroup
Elementary abelian group
Finite normal subgroupNormal subgroup
Finite group
Finitely generated normal subgroupNormal subgroup
Finitely generated group
Group in which every automorphism is innerNormal subgroup
Central factor
Automorphism of a group
Inner automorphism
Group in which every nontrivial normal subgroup has finite indexNormal subgroup
Subgroup of finite index
Group in which every normal subgroup is a central factorNormal subgroup
Central factor
Group in which every normal subgroup is a direct factorNormal subgroup
Direct factor
Group in which every normal subgroup is characteristicNormal subgroup
Characteristic subgroup
Transitively normal subgroup
Automorphism of a group
Normal automorphism
Group in which every normal subgroup is fully invariantNormal subgroup
Fully invariant subgroup
Group in which every normal subgroup is powering-invariantNormal subgroup
Powering-invariant subgroup
Group in which every permutable subgroup is normalPermutable subgroup
Normal subgroup
Group in which every pronormal subgroup is normalPronormal subgroup
Normal subgroup
Group in which every retract is a direct factorNormal subgroup
Retract
Direct factor
Group in which every subgroup is pronormalPronormal subgroup
Normal subgroup
Hamiltonian operator
Group whose automorphism group is abelianabelian automorphism group
any two automorphisms commute
Automorphism group of a group
Abelian group
Normal subgroup
Normal subgroup contained in centralizer of derived subgroup
Group whose inner automorphism group is central in automorphism groupInner automorphism group
Central subgroup
Automorphism group of a group
Inner automorphism
Central automorphism
Normal subgroup
Commutator-in-center subgroup
Groups embeddable as normal subgroups in a finite group with a common complementNormal subgroup
Permutable complements
Normal complement
Hall subgroup of normal subgroupHall subgroup
Normal subgroup
Hereditarily normal subgroupTransitively normal subgroup
Dedekind group
Normal subgroup
Hereditarily operator