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