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

Abstract

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.

Keywords:

• Group algebra
• representation dimension
• separable equivalence

Acknowledgments

I would like to thank Jeremy Rickard for all of his help; without his guidance this work could not have been possible. I would also like to thank the article reviewers for many helpful comments and suggestions.