# Elementary abelian subgroup of maximum rank

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]

This article is about a maximality notion among subgroups, related to abelianness or small class, in a group of prime power order.

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## Statement

A subgroup of a group of prime power order is termed an **elementary abelian subgroup of maximum rank** or an **elementary abelian subgroup of maximum order** if it is elementary abelian as a group and there is no elementary abelian subgroup of the group having greater order than it.