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

Linckelmann showed in 2011 that a group algebra is separably equivalent to the group algebra of its Sylow p-subgroups. 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 $|P|$.