NSCFN-subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

Symbol-free definition

A subgroup of a group is termed a NSCFN-subgroup if it is normal, fully normalized and self-centralizing in the whole group.

Definition with symbols

A subgroup H of a group G is termed a NSCFN-subgroup if H \triangleleft G, H is fully normalized in G, and C_G(H) \le H.

Equivalently, H is a NSCFN-subgroup of G if H is a normal subgroup of G, and the induced homomorphism G \to \operatorname{Aut}(H) induced by the conjugation action is surjective with kernel equal to Z(H).