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The Sylow p-subgroups of the symmetric group S_p^n satisfy the appropriategeneralization of Maschke's Theorem to the case of a p'-group acting on a (notnecessarily abelian) p-group. Moreover, some known results about the Sylowp-subgroups of S_p^n are stated in a form that is true for all primes p.

The Maschke property for the Sylow p-subgroups of the symmetric group S_p^n