# Core-free permutable subgroup

From Groupprops

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: core-free subgroup and permutable subgroup

View other subgroup property conjunctions | view all subgroup properties

## Contents

## Definition

A subgroup of a group is termed a **core-free permutable subgroup** if it is both core-free (i.e., its normal core is trivial) and permutable (i.e., quasinormal).