In this article, we present an upper bound on the representation dimension of the group algebra of a group with an elementary abelian Sylow p-subgroup. Specifically, if k is a field of characteristic p and G is a group with elementary abelian Sylow p-subgroup P, we prove that the representation dimension of kG is bounded above by the order of P. Key to proving this theorem is the separable equivalence between the two algebras and some nice properties of Mackey decomposition.
|Number of pages||13|
|Journal||Communications in Algebra|
|Publication status||Published - 9 Jul 2019|
- Group algebra
- representation dimension
- separable equivalence