# Core-free subnormal 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 subnormal subgroup

View other subgroup property conjunctions | view all subgroup properties

## Contents

## Definition

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