# Semipermutable 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 |

## Contents

## Definition

### Symbol-free definition

A subgroup of a finite group is termed **semipermutable** if it permutes with every subgroup whose order is relatively prime to it.

### Definition with symbols

A subgroup of a finite group is termed **semipermutable** if for any group such that the orders of and are relatively prime, .