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On strongly associative group algebras of p-solvable groups

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. We characterize the strongly associative modular group algebras FH with H being a p-solvable group.