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 Mat. Sb. (N.S.), 1979, Volume 108(150), Number 2, Pages 187–211 (Mi msb2279)

Crossed group rings of finite groups and rings of $p$-adic integers with finitely many indecomposable integral representations

L. F. Barannik, P. M. Gudivok

Abstract: Let $F$ be a finite extension of the field $Q_p$ of rational $p$-adic numbers, $R$ the ring of all integral elements of $F$, $R^*$ the multiplicative group of $R$, $G$ a finite group, and $\Lambda=(G,R,\lambda)$ the crossed group ring of $G$ and $R$ with the factor system $\{\lambda_{a,b}\}$ ($\lambda_{a,b}\in R^*$; $a,b\in G$). A classification is given of the rings $\Lambda$ for which the number of indecomposable $R$-representations is finite. When $\Lambda$ is a group ring, this problem was solved in papers by Faddeev, Borevich, Gudivok, Yakobinskii, and others.
Bibliography: 22 titles.

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English version:
Mathematics of the USSR-Sbornik, 1980, 36:2, 173–194

Bibliographic databases:

UDC: 519.49
MSC: 20C05, 20C10

Citation: L. F. Barannik, P. M. Gudivok, “Crossed group rings of finite groups and rings of $p$-adic integers with finitely many indecomposable integral representations”, Mat. Sb. (N.S.), 108(150):2 (1979), 187–211; Math. USSR-Sb., 36:2 (1980), 173–194

Citation in format AMSBIB
\Bibitem{BarGud79} \by L.~F.~Barannik, P.~M.~Gudivok \paper Crossed group rings of finite groups and rings of $p$-adic integers with finitely many indecomposable integral representations \jour Mat. Sb. (N.S.) \yr 1979 \vol 108(150) \issue 2 \pages 187--211 \mathnet{http://mi.mathnet.ru/msb2279} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=525837} \zmath{https://zbmath.org/?q=an:0433.16011|0402.16012} \transl \jour Math. USSR-Sb. \yr 1980 \vol 36 \issue 2 \pages 173--194 \crossref{https://doi.org/10.1070/SM1980v036n02ABEH001781} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980KM22500003}