An upper bound for the representation dimension of group algebras with an elementary abelian Sylow $p$-subgroup

Abstract

Linckelmann showed in [Lin11] that a group algebra is separably equivalent to the group algebra of its Sylow p-subgroup. In this article we use this relationship, together with Mackey decomposition, to demonstrate that a group algebra of a group with an elementary abelian Sylow p-subgroup P, has representation dimension at most |P|.