# Subgroup with canonical abelianization

From Groupprops

(Redirected from Subgroup with canonical Abelianization)

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

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]

## Definition

A **subgroup with canonical Abelianization** is a subgroup satisfying the following property: any inner automorphism of the whole group that sends the subgroup to itself, restricts to an IA-automorphism of the subgroup.

## Formalisms

### In terms of the in-normalizer operator

This property is obtained by applying the in-normalizer operator to the property: IA-balanced subgroup

View other properties obtained by applying the in-normalizer operator