# Normalizer subgroup

From Groupprops

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]

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## Definition

### Symbol-free definition

A subgroup of a group is termed a **normalizer subgroup** if it occurs as the normalizer of some subset (or equivalently, of some subgroup).

### Definition with symbols

A subgroup of a group is termed a **normalizer subgroup** if there is a subgroup of such that .