Weakly characteristic subgroup

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Definition

Definition with symbols

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