# Core-free permutable subgroup

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

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## 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).