# Normalizer of a subset of a group

From Groupprops

## Definition

Let be a group and be a subset of . The **normalizer** (**normaliser**) of in , denoted is defined as:

.

Equivalently, it is the isotropy of under the action of on the set of subsets of by conjugation.

We typically use the term **normalizer** for normalizer of a subgroup, i.e., where the subset we start with is a subgroup of .