# Group of prime power order having a maximal elementary abelian subgroup of prime-square order

From Groupprops

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Definition

Let be a group of prime power order, i.e., a finite -group for some prime number . We say that has a maximal elementary abelian subgroup of prime-square order if it satisfies the following equivalent conditions:

- There exists an elementary abelian subgroup of of order that is not contained in any bigger elementary abelian subgroup of .
- There exists an elementary abelian subgroup of of order such that .
- There exists an element such that is elementary abelian of order .