# Strongly closed subgroup

From Groupprops

This article describes a property that can be evaluated for a triple of a group, a subgroup of the group, and a subgroup of that subgroup.

View other such properties

## Contents

## Definition

### Definition with symbols

Let be groups. Then, is said to be **strongly closed** in with respect to if any -conjugate of an element of , which lies inside , in fact lies inside . In other words, for any :

.

The term is typically used for the situation where is a Sylow subgroup of . The particular case can also be generalized to the notion of a strongly closed subgroup for a fusion system.