Ukrainian Mathematical Bulletin

Volume 2, Issue 1, 2005 pp. 67-75.

On Representations of a Direct Product of Finite Groups over Complete Discrete Valuation Rings

Authors: Petro M. Gudyvok
Author institution: Department of Mathematics, Uzhgorod National University, 14 Universitetskaya St., Uzhgorod 88016, Ukraine

Summary: Let $G=H \times B$ be the direct product of finite groups $H$ and $B$ ($H$ is a Sylow $p$-subgroup of the group $G$), let $K$ be a complete discrete normed ring with residue field of characteristic $p$, and let $KG$ be the group ring of the group $G$ over the ring $K$. $KG$-modules are understood as $KG$-modules that are free $K$-modules of finite rank. We establish conditions under which an arbitrary indecomposable $KG$-module is representable in the form of an external tensor product of an indecomposable $KH$-module and an irreducible $KB$-module. Note that the case where $K$ is a field of characteristic $p$ was considered in \cite{G2}, \cite{G3}, and \cite{Bl1}.

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