Normalizer subgroup

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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VIEW FACTS THAT:use, or start with, a subgroup satisfying the property|prove, or show that, a subgroup satisfies the property

This article is about a standard (though not very rudimentary) definition in group theory. The article text may, however, contain more than just the basic definition
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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 $K$ of a group $G$ is termed a normalizer subgroup if there is a subgroup $H$ of $G$ such that $K=N_G(H)$.

Relation with other properties

Stronger properties

• Self-normalizing subgroup