On the Isomorphic Group Algebras of Isotype Subgroups of Warfield Abelian Groups

Abstract

A new class of global mixed Abelian groups, called W-groups, is defined. The following isomorphism theorem for commutative modular group algebras of such groups is proved: If G is a p-mixed μ-elementary W-group for some arbitrary ordinal μ, then the F-isomorphism between the group algebras FG and FH of prime characteristic p for any group H implies that G and H are isomorphic.