# Sylow-closure

From Groupprops

Template:Prime-parametrized sdf

## Definition

### Symbol-free definition

A subgroup of a group is termed a **Sylow-closure** if it occurs as the normal closure of a Sylow subgroup.

In the prime parametrized sense, the -Sylow closure is the normal closure of any -Sylow subgroup (note that since all the Sylow subgroups are conjugate, this is a unique subgroup).