[[defining ingredient::Normal subgroup]]

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	Quick phrase	Defining ingredient
2-subnormal subgroup		Normal subgroup Normal closure Normalizer of a subgroup Conjugate subgroups Normal core of normalizer Normal core
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 Diagonal-in-square operator Normal subgroup
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
Aut-abelian group	abelian automorphism group any two automorphisms commute	Automorphism group of a group Abelian group Normal subgroup Normal subgroup contained in centralizer of derived subgroup
Aut-abelian normal subgroup		Normal subgroup Aut-abelian group
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
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
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

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