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

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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.

Bibliographical metadata

Original languageEnglish
JournalCommunications in Algebra
Early online date9 Jul 2019
DOIs
Publication statusPublished - 2019