Given a partial action alpha 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 *(alpha) G. If FH *(alpha) G is associative for any G and any alpha, then FH is called strongly associative. We characterize the strongly associative modular group algebras FH with H being a p-solvable group.
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