# Abelian normal subgroup of maximum order

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]

## Contents

## Definition

A subgroup of a group of prime power order is termed an **abelian normal subgroup of maximum order** if it is an abelian normal subgroup (specifically, an abelian normal subgroup of group of prime power order) and there is no abelian normal subgroup of of larger order than .