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

TL;DR

This paper investigates the Maschke property for Sylow p-subgroups of symmetric groups, extending classical results to non-abelian cases and general primes, revealing new structural insights.

Contribution

It generalizes Maschke's Theorem to Sylow p-subgroups of symmetric groups acting on p-groups, including non-abelian cases, and unifies known results across all primes.

Findings

Sylow p-subgroups satisfy a generalized Maschke property

Results are applicable to non-abelian p-groups

Some known results are extended to all primes p

Abstract

The Sylow p-subgroups of the symmetric group S_p^n satisfy the appropriate generalization of Maschke's Theorem to the case of a p'-group acting on a (not necessarily abelian) p-group. Moreover, some known results about the Sylow p-subgroups of S_p^n are stated in a form that is true for all primes p.