# Abelian normal subgroup of maximum rank

From Groupprops

## Definition

A subgroup of a group of prime power order is termed an **Abelian normal subgroup of maximum rank** if it is an Abelian normal subgroup (i.e., it is an Abelian group and is a normal subgroup) and its rank equals the maximum of the ranks of Abelian normal subgroups. Equivalently, it is an Abelian normal subgroup whose rank equals the normal rank of the whole group.