# Abelian subgroup of maximum order which is normal

From Groupprops

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: abelian subgroup of maximum order and abelian normal subgroup of group of prime power order

View other subgroup property conjunctions | view all subgroup properties

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: abelian subgroup of maximum order and abelian normal subgroup

View other subgroup property conjunctions | view all subgroup properties

## Definition

Suppose is a group of prime power order, i.e., is a finite p-group for some prime number . Suppose is a subgroup of . We say that is an **abelian subgroup of maximum order which is normal** if is an abelian subgroup of maximum order in and is also a normal subgroup of .