the maschke property for the sylow p-groups of the symmetric group spn

‎‎in this paper we prove that the maschke property holds for coprime actions on some important classes of p-groups like‎: ‎metacyclic p-groups‎, ‎p-groups of p-rank two for p>3 and some weaker property holds in the case of regular p-groups‎. ‎the main focus will be the case of coprime actions on the iterated wreath product pn of cyclic groups of order p‎, ‎i.e‎. ‎on sylow p-subgroups of the symmetric groups spn‎, ‎where we also prove that a stronger form of the maschke property holds‎. ‎these results contribute to a future possible classification of all p-groups with the maschke property‎. ‎we apply these results to describe which normal partition subgroups of pn have a complement‎. ‎in the end we also describe abelian subgroups of pn of largest size‎.