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Mat. Sb. (N.S.), 1970, Volume 82(124), Number 3(7), Pages 423–443 (Mi msb3459)  

This article is cited in 2 scientific papers (total in 2 papers)

Projective representations of finite groups over number rings

L. F. Barannik, P. M. Gudivok


Abstract: We solve the problem of finding the number $n(R,G)$ of nondecomposable projective representations of a finite group $G$ over the ring $R$ of all integers of a finite extension $F$ of the field of rational $p$-adic numbers $Q$. Also we clear up the question as to when all indecomposable projective $R$-representations of a group $G$ are realized by left ideals of crossed group rings of the group $G$ and the ring $R$. We note that for ordinary $R$-representations of a group $G$ the problem of the finiteness of the number $n(R,G)$ was investigated by S. D. Berman, I. Reiner, A. Heller, H. Yacobinski and one of the authors of the present article.
Bibliography: 30 titles.

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English version:
Mathematics of the USSR-Sbornik, 1970, 11:3, 391–410

Bibliographic databases:

UDC: 519.44
MSC: 20C25, 20C05, 20G25, 20C11, 13M10
Received: 01.10.1969

Citation: L. F. Barannik, P. M. Gudivok, “Projective representations of finite groups over number rings”, Mat. Sb. (N.S.), 82(124):3(7) (1970), 423–443; Math. USSR-Sb., 11:3 (1970), 391–410

Citation in format AMSBIB
\Bibitem{BarGud70}
\by L.~F.~Barannik, P.~M.~Gudivok
\paper Projective representations of finite groups over number rings
\jour Mat. Sb. (N.S.)
\yr 1970
\vol 82(124)
\issue 3(7)
\pages 423--443
\mathnet{http://mi.mathnet.ru/msb3459}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=277622}
\zmath{https://zbmath.org/?q=an:0277.20012}
\transl
\jour Math. USSR-Sb.
\yr 1970
\vol 11
\issue 3
\pages 391--410
\crossref{https://doi.org/10.1070/SM1970v011n03ABEH001298}


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    Citing articles on Google Scholar: Russian citations, English citations
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    Erratum

    This publication is cited in the following articles:
    1. P. M. Gudivok, “On the number of indecomposable integral $p$-adic representations of crossed group rings”, Math. USSR-Sb., 20:1 (1973), 27–51  mathnet  crossref  mathscinet  zmath
    2. 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  mathnet  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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