Semantic search

	Quick phrase	Defining ingredient
2-subnormal subgroup		Normal 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 subgroup		Normal subgroup 2-subnormal subgroup
4-subnormal subgroup		Subnormal subgroup Subnormal depth 2-subnormal subgroup Normal subgroup 3-subnormal subgroup
Abelian group		Center Derived subgroup Normal subgroup Diagonal-in-square operator
Abelian normal subgroup		Normal subgroup Abelian group
Abelian normal subgroup of maximum rank		Abelian normal subgroup Abelian group Normal subgroup Rank of a p-group Normal rank of a p-group
Almost normal subgroup		Normal subgroup Subgroup of finite index Normalizer of a subgroup Index of a subgroup Conjugate subgroups
Almost subnormal subgroup		Normal subgroup Subgroup of finite index
Automorph-conjugate subgroup		Automorphic subgroups Conjugate subgroups Normal subgroup Normalizer of a subgroup
Automorphism-faithful normal subgroup		Automorphism-faithful subgroup Normal subgroup
C-closed normal subgroup		C-closed subgroup Normal subgroup
Central factor of normal subgroup		Central factor Normal subgroup Normal closure
Centralizer-free normal subgroup		Centralizer-free subgroup Normal subgroup
Class two normal subgroup		Normal subgroup Group of nilpotency class two
Closed normal subgroup		Closed subgroup of semitopological group Normal subgroup
Commutator of a normal subgroup and a subset		Normal subgroup Commutator of two subsets Commutator
Commutator-in-center subgroup		Normal subgroup Commutator-in-centralizer subgroup
Complete direct factor		Direct factor Complete group Normal subgroup Complemented normal subgroup
Complete group		Normal subgroup Direct factor
Completely divisibility-closed normal subgroup		Completely divisibility-closed subgroup Normal subgroup
Conjugacy-closed normal subgroup		Conjugacy-closed subgroup Normal subgroup
Coprime automorphism-faithful normal subgroup		Coprime automorphism-faithful subgroup Normal subgroup
Coprime automorphism-invariant normal subgroup		Coprime automorphism-invariant subgroup Normal subgroup
Coprime automorphism-invariant normal subgroup of group of prime power order		Coprime 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 subgroup		Normal subgroup Cyclic group
Dedekind group	every 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 subgroup		Normal subgroup Dedekind group
Direct factor	factor in internal direct product normal with normal complement has centralizing complement	Internal direct product Normal subgroup Normal complement Retract
Direct factor of normal subgroup		Direct factor Normal subgroup Normal closure
Divisible normal subgroup		Normal subgroup Divisible group
Elementary abelian normal subgroup		Normal subgroup Elementary abelian group
Finite normal subgroup		Normal subgroup Finite group
Finitely generated normal subgroup		Normal subgroup Finitely generated group
Group in which every automorphism is inner		Normal subgroup Central factor Automorphism of a group Inner automorphism
Group in which every nontrivial normal subgroup has finite index		Normal subgroup Subgroup of finite index
Group in which every normal subgroup is a central factor		Normal subgroup Central factor
Group in which every normal subgroup is a direct factor		Normal subgroup Direct factor
Group in which every normal subgroup is characteristic		Normal subgroup Characteristic subgroup Transitively normal subgroup Automorphism of a group Normal automorphism
Group in which every normal subgroup is fully invariant		Normal subgroup Fully invariant subgroup
Group in which every normal subgroup is powering-invariant		Normal subgroup Powering-invariant subgroup
Group in which every permutable subgroup is normal		Permutable subgroup Normal subgroup
Group in which every pronormal subgroup is normal		Pronormal subgroup Normal subgroup
Group in which every retract is a direct factor		Normal subgroup Retract Direct factor
Group in which every subgroup is pronormal		Pronormal subgroup Normal subgroup Hamiltonian operator
Group whose automorphism group is abelian	abelian 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 group		Inner 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 complement		Normal subgroup Permutable complements Normal complement
Hall subgroup of normal subgroup		Hall subgroup Normal subgroup
Hereditarily normal subgroup		Transitively normal subgroup Dedekind group Normal subgroup Hereditarily operator
Homocyclic normal subgroup		Normal subgroup Homocyclic group

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