# Finite isomorph-free subgroup

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: isomorph-free subgroup with a group property (itself viewed as a subgroup property): finite group

View a complete list of such conjunctions

## Contents

## Definition

A subgroup of a group is termed a **finite isomorph-free subgroup** if it satisfies the following equivalent conditions:

- It is a finite group and is also an isomorph-free subgroup of the whole group.
- It is a finite group and is also an isomorph-containing subgroup of the whole group.