[[defining ingredient::Characteristic subgroup]]

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	Quick phrase	Defining ingredient
ACIC-group		Automorph-conjugate subgroup Characteristic subgroup
Abelian characteristic subgroup		Characteristic subgroup Abelian group
CSCFN-subgroup		Characteristic subgroup Self-centralizing subgroup Fully normalized subgroup
Characteristic AEP-subgroup		Characteristic subgroup AEP-subgroup
Characteristic central factor		Characteristic subgroup Central factor
Characteristic closure	smallest characteristic subgroup containing intersection of all characteristic subgroups containing join of all automorphic subgroups	Characteristic subgroup Automorphic subgroups Subgroup generated by a subset
Characteristic core		Characteristic subgroup Automorphic subgroups Automorphism of a group
Characteristic direct factor		Characteristic subgroup Direct factor
Characteristic maximal subgroup of group of prime power order		Characteristic subgroup Maximal subgroup of group of prime power order
Characteristic subgroup of Sylow subgroup		Characteristic subgroup Sylow subgroup
Characteristic subgroup of abelian group		Characteristic subgroup Abelian group
Characteristic subgroup of direct factor		Characteristic subgroup Direct factor
Characteristic subgroup of finite group		Characteristic subgroup Finite group Strictly characteristic subgroup Injective endomorphism-invariant subgroup
Characteristic subgroup of group of prime power order		Characteristic subgroup Group of prime power order
Characteristic subgroup of pronormal subgroup		Characteristic subgroup Pronormal subgroup
Characteristic transitively normal subgroup		Characteristic subgroup Transitively normal subgroup CEP-subgroup
Characteristic-extensible automorphism		Qualified extensibility operator Characteristic subgroup
Characteristically complemented characteristic subgroup		Characteristically complemented subgroup Characteristic subgroup Permutable complements
Characteristically complemented subgroup		Retraction Characteristic subgroup Permutable complements Lattice complements
Characteristically simple group		Characteristic subgroup Characteristic closure Characteristic core Simple group operator

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