TY - JOUR
T1 - An upper bound for the representation dimension of group algebras with elementary abelian Sylow p-subgroups
AU - Peacock, Simon
PY - 2019/7/9
Y1 - 2019/7/9
N2 - 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.
AB - 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.
KW - Group algebra
KW - representation dimension
KW - separable equivalence
UR - http://www.scopus.com/inward/record.url?scp=85068708065&partnerID=8YFLogxK
U2 - 10.1080/00927872.2019.1632327
DO - 10.1080/00927872.2019.1632327
M3 - Article (Academic Journal)
AN - SCOPUS:85068708065
SN - 0092-7872
JO - Communications in Algebra
JF - Communications in Algebra
ER -