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 Mat. Sb. (N.S.), 1973, Volume 91(133), Number 1(5), Pages 27–49 (Mi msb3102)

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

P. M. Gudivok

Abstract: 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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English version:
Mathematics of the USSR-Sbornik, 1973, 20:1, 27–51

Bibliographic databases:

UDC: 519.49
MSC: Primary 20C10; Secondary 16A18

Citation: P. M. Gudivok, “On the number of indecomposable integral $p$-adic representations of crossed group rings”, Mat. Sb. (N.S.), 91(133):1(5) (1973), 27–49; Math. USSR-Sb., 20:1 (1973), 27–51

Citation in format AMSBIB
\Bibitem{Gud73} \by P.~M.~Gudivok \paper On~the number of indecomposable integral $p$-adic representations of crossed group rings \jour Mat. Sb. (N.S.) \yr 1973 \vol 91(133) \issue 1(5) \pages 27--49 \mathnet{http://mi.mathnet.ru/msb3102} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=332863} \zmath{https://zbmath.org/?q=an:0338.20004} \transl \jour Math. USSR-Sb. \yr 1973 \vol 20 \issue 1 \pages 27--51 \crossref{https://doi.org/10.1070/SM1973v020n01ABEH001827} 

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This publication is cited in the following articles:
1. L. F. Barannik, P. M. Gudivok, “Crossed group rings of finite groups and rings of $p$-adic integers with finitely many indecomposable integral representations”, Math. USSR-Sb., 36:2 (1980), 173–194
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