On Strongly Associative Group Algebras

Abstract

Given a partial action α of a group G on the group algebra FH, where H is a finite group and F is a field whose characteristic p divides the order of H, we investigate the associativity question of the partial crossed product FH*_α G. If FH*_α G is associative for any G and any α, then FH is called “strongly associative.” Using a result of Dokuchaev and Exel (2005) we characterize the strongly associative modular group algebras FH for several classes of groups H.

Key Words:

• Group algebras
• Partial actions

2000 Mathematics Subject Classification:

• Primary 16S34
• Secondary 20C05

ACKNOWLEDGMENTS

The present article is based on a part of my Ph.D. thesis (Lopes, 2005) which was directed by Prof. M. Dokuchaev at the IME-USP (São Paulo, Brazil). I wish to thank him for his attention and encouragement. This article is supported by PICDT/CAPES of Brazil.

Notes

Communicated by I. P. Shestakov.