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Izv. Akad. Nauk SSSR Ser. Mat., 1967, Volume 31, Issue 4, Pages 799–834 (Mi izv2566)  

This article is cited in 5 scientific papers (total in 5 papers)

Representations of finite groups over number rings

P. M. Gudivok


Abstract: Let $R'$ be the ring of integers of a finite extension $F'$ of the field of rational $p$-adic numbers $Q_p$, and let $G$ be a finite group. All groups $G$ and fields $F'$ are found such that the number of indecomposable representations of $G$ over $R'$ is finite. In addition, we investigate the problem of complete reducibility of a matrix $R'$-representation of an abelian $p$-group, all of whose irreducible components are $F'$-equivalent.

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English version:
Mathematics of the USSR-Izvestiya, 1967, 1:4, 773–805

Bibliographic databases:

UDC: 519.4
MSC: 20C11, 20Kxx, 20F18, 11R04, 20C12
Received: 19.04.1966

Citation: P. M. Gudivok, “Representations of finite groups over number rings”, Izv. Akad. Nauk SSSR Ser. Mat., 31:4 (1967), 799–834; Math. USSR-Izv., 1:4 (1967), 773–805

Citation in format AMSBIB
\Bibitem{Gud67}
\by P.~M.~Gudivok
\paper Representations of finite groups over number rings
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1967
\vol 31
\issue 4
\pages 799--834
\mathnet{http://mi.mathnet.ru/izv2566}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=218468}
\zmath{https://zbmath.org/?q=an:0269.20007}
\transl
\jour Math. USSR-Izv.
\yr 1967
\vol 1
\issue 4
\pages 773--805
\crossref{https://doi.org/10.1070/IM1967v001n04ABEH000589}


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

    This publication is cited in the following articles:
    1. L. F. Barannik, P. M. Gudivok, “Projective representations of finite groups over number rings”, Math. USSR-Sb., 11:3 (1970), 391–410  mathnet  crossref  mathscinet  zmath
    2. Yu. A. Drozd, V. V. Kirichenko, “Primary orders with a finite numbers of indecomposable representations”, Math. USSR-Izv., 7:4 (1973), 711–732  mathnet  crossref  mathscinet  zmath
    3. P. M. Gudivok, V. P. Rud'ko, “On modular and integral representation algebras on finite groups”, Math. USSR-Izv., 7:5 (1973), 963–989  mathnet  crossref  mathscinet  zmath
    4. P. M. Gudivok, S. F. Goncharova, V. P. Rud'ko, “Finite-dimensional algebras of integral $p$-adic representations of finite groups”, Math. USSR-Sb., 23:3 (1974), 336–361  mathnet  crossref  mathscinet  zmath
    5. 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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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