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Zap. Nauchn. Sem. LOMI, 1979, Volume 86, Pages 30–33 (Mi znsl1819)  

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

Description of subgroups of the full linear group over a semilocal ring that contain the group of diagonal matrices

N. A. Vavilov


Abstract: It has been proved (Ref. Zh. Mat., 1978, 9A237) that for a semilocal ring $\Lambda$ in which each residue field of the center contains at least seven elements we have the following description of subgroups of the full linear group $GL(n,\Lambda)$ that contain the group of diagonal matrices: for each such subgroup $H$ there is a uniquely defined $D$-net of ideals $\sigma$ (Ref. Zh. Mat., 1977, 2A288) such that $G(\sigma)\leqslant h\leqslant N(\sigma)$, ,where $N(\sigma)$ is the normalizer of the $\sigma$-net subgroup $G(\sigma)$. It is noted that this result is also true under the following weaker assumption: a decomposition of a quotient ring of the ring $\Lambda$ into a direct sum of full matrix rings over skew fields does not contain skew fields with centers of less than seven elements or the ring of second-order matrices over the field of two elements.

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English version:
Journal of Soviet Mathematics, 1981, 17:4, 1960–1963

Bibliographic databases:

UDC: 519.46

Citation: N. A. Vavilov, “Description of subgroups of the full linear group over a semilocal ring that contain the group of diagonal matrices”, Algebraic numbers and finite groups, Zap. Nauchn. Sem. LOMI, 86, "Nauka", Leningrad. Otdel., Leningrad, 1979, 30–33; J. Soviet Math., 17:4 (1981), 1960–1963

Citation in format AMSBIB
\Bibitem{Vav79}
\by N.~A.~Vavilov
\paper Description of subgroups of the full linear group over a semilocal ring that contain the group of diagonal matrices
\inbook Algebraic numbers and finite groups
\serial Zap. Nauchn. Sem. LOMI
\yr 1979
\vol 86
\pages 30--33
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl1819}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=535477}
\zmath{https://zbmath.org/?q=an:0462.20042|0418.20042}
\transl
\jour J. Soviet Math.
\yr 1981
\vol 17
\issue 4
\pages 1960--1963
\crossref{https://doi.org/10.1007/BF01465452}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Panin, A. V. Yakovlev, “Teoriya Galua dlya odnogo klassa dedekindovykh struktur”, Voprosy teorii predstavlenii algebr i grupp. 5, Zap. nauchn. sem. POMI, 236, POMI, SPb., 1997, 133–148  mathnet  mathscinet  zmath; A. A. Panin, A. V. Yakovlev, “The Galois theory for a class of modular lattices”, J. Math. Sci. (New York), 95:2 (1999), 2126–2135  crossref
    2. A. V. Schegolev, “Nadgruppy blochno-diagonalnykh podgrupp giperbolicheskoi unitarnoi gruppy nad kvazi-konechnym koltsom: osnovnye rezultaty”, Voprosy teorii predstavlenii algebr i grupp. 29, Zap. nauchn. sem. POMI, 443, POMI, SPb., 2016, 222–233  mathnet  mathscinet
  • Записки научных семинаров ПОМИ
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