On the number of indecomposable integral $p$-adic representations of crossed group rings

P. M. Gudivok

Sbornik. Mathematics, Tome 20 (1973) no. 1, pp. 27-51

Résumé

Let $G$ be a finite group, $Z_p$ the ring of $p$-adic integers, $Z_p^*$ the multiplicative group of $Z_p$ and $(G,Z_p,\Lambda)$ the crossed product group ring by the factor set $\{\lambda_{a, b}\}$ ($\lambda_{a, b}\in Z_p^*;$ $a,b\in G$). We find all rings $\Lambda=(G,Z_p,\lambda)$ such that the number of indecomposable $Z_p$-representations of $\Lambda$ is finite. We note that in case $\Lambda$ is the group ring $Z_pG$ the analogous problem was solved by Berman, Heller, Reiner and the author. Bibliography: 22 titles.

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