Finite groups of matrices over group rings

Cliff, Gerald; Weiss, Alfred

doi:10.1090/S0002-9947-99-02319-3

Finite groups of matrices over group rings
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by Gerald Cliff and Alfred Weiss PDF

Trans. Amer. Math. Soc. 352 (2000), 457-475 Request permission

Abstract:

We investigate certain finite subgroups $\Gamma$ of $GL_{n}(\mathbf {Z}\Pi )$, where $\Pi$ is a finite nilpotent group. Such a group $\Gamma$ gives rise to a $\mathbf {Z}[\Gamma \times \Pi ]$-module; we study the characters of these modules to limit the structure of $\Gamma$. We also exhibit some exotic subgroups $\Gamma$.

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