Weakly characteristic 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

Definition with symbols

A subgroup H of a group G is termed weakly characteristic in G if for any \sigma \in \operatorname{Aut}(G), \sigma(H) \le N_G(H) implies \sigma(H) \le H. Here, N_G(H), denotes the normalizer of H in G.

Relation with other properties

Stronger properties

Weaker properties