Ukrainian Mathematical Bulletin

Volume 3, Issue 3, 2006 pp. 291-300.

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

Authors: Peter Danchev
Author institution: Mathematical Department, Plovdiv University, 4000 Plovdiv, Bulgaria pvdanchev@yahoo.com

Summary: 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 $\mu$-elementary $W$-group for some arbitrary ordinal $\mu$, 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. This strengthens our recent results in (Bol. Soc. Mat. Mexicana, 2004) and (Acta Math. Sinica, 2005) as well as results due to Ullery in (Proc. Amer. Math. Soc., 1988 and 1990) and (Comm. Algebra, 1989).

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