On the Unit Groups of Commutative Modular Group Algebras of KT-Groups

Abstract

Let G be an abelian group and let R be a commutative indecomposable p-perfect ring with identity of prime characteristic p. Denote by RG the group ring of G over R and by V(RG) the group of normalized units (i.e., the units of augmentation 1) of the group ring RG. Warfield [16] introduces the concept KT-module A over a discrete valuation ring R and invariants h(α, A) of this module for limit ordinals α. We compute the invariants h(α, V(RG)) of the group V(RG). Our result correct essential mistakes of the result in this direction of Danchev [4].