# Weakly characteristic subgroup

## Contents

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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 $G$.