# Automorph-permutable 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]

This is a variation of permutability|Find other variations of permutability |

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

## Definition

### Symbol-free definition

A subgroup of a group is termed **automorph-permutable** if it permutes with any subgroup obtained as the image of it under an automorphism of the whole group.

### Definition with symbols

A subgroup of a group is termed **automorph-permutable** if for any automorphism of , .