We show that the number of maximal abelian subgroups of a finite p-group is congruent to 1 modulo p. Furthermore, if p> 2 , the same can be said for the maximal elementary abelian subgroups, and more generally, for the maximal abelian subgroups of any given p-power exponent.
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- Exponent of group
- Maximal abelian subgroup