Isomorphic Commutative Group Algebras of p-Mixed Warfield Groups

Abstract

Let G be a p-mixed Warfield Abelian group and F a field of char F = p ≠ 0. It is proved that if for any group H the group algebras FH and FG are F-isomorphic, then H is isomorphic to G. This presentation enlarges a result of W. May argued when G is p-local Warfield Abelian and published in Proc. Amer. Math. Soc. (1988).