Elementary Abelian normal subgroup of maximum rank

Definition

A subgroup of a group of prime power order is termed an elementary Abelian normal subgroup of maximum rank if it is an elementary Abelian normal subgroup (i.e., it is elementary Abelian as a group and is also a [[defining ingredient::normal subgroup|normal subgroup of the whole group) whose rank (i.e., the dimension as a vector space over the prime field) is the maximum of the ranks of elementary Abelian normal subgroups in the whole group.