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Zap. Nauchn. Sem. POMI, 2007, Volume 343, Pages 33–53 (Mi znsl110)  

This article is cited in 4 scientific papers (total in 4 papers)

Subgroups of $\operatorname{SL}_n$ over a semilocal ring

N. A. Vavilov

Saint-Petersburg State University

Abstract: In the present paper we prove that if $R$ is a commutative semi-local ring all of whose residue fields contain at least $3n+2$ elements, then for every subgroup $H$ of the special linear group $\operatorname{SL}(n,R)$, $n\ge 3$, containing the diagonal subgroup $\operatorname{SD}(n,R)$ there exists a unique $D$-net $\sigma$ of ideals $R$ such that $\mathrm{G}(\sigma)\le H\le N_{\mathrm{G}}(\sigma)$. In the works by Z. I. Borewicz and the author similar results were established for $\operatorname{GL}_n$ over semi-local rings and for $\operatorname{SL}_n$ over fields. Later I. Hamdan obtained similar description for a very special case of uniserial rings.

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English version:
Journal of Mathematical Sciences (New York), 2007, 147:5, 6995–7004

Bibliographic databases:

UDC: 512.5
Received: 19.10.2006

Citation: N. A. Vavilov, “Subgroups of $\operatorname{SL}_n$ over a semilocal ring”, Problems in the theory of representations of algebras and groups. Part 15, Zap. Nauchn. Sem. POMI, 343, POMI, St. Petersburg, 2007, 33–53; J. Math. Sci. (N. Y.), 147:5 (2007), 6995–7004

Citation in format AMSBIB
\Bibitem{Vav07}
\by N.~A.~Vavilov
\paper Subgroups of $\operatorname{SL}_n$ over a semilocal ring
\inbook Problems in the theory of representations of algebras and groups. Part~15
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 343
\pages 33--53
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl110}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2469412}
\elib{http://elibrary.ru/item.asp?id=9595465}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 147
\issue 5
\pages 6995--7004
\crossref{https://doi.org/10.1007/s10958-007-0525-3}
\elib{http://elibrary.ru/item.asp?id=13545992}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-36148993298}


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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. N. A. Vavilov, “O podgruppakh simplekticheskoi gruppy, soderzhaschikh subsystem subgroup”, Voprosy teorii predstavlenii algebr i grupp. 16, Zap. nauchn. sem. POMI, 349, POMI, SPb., 2007, 5–29  mathnet  mathscinet  elib; N. A. Vavilov, “On subgroups of symplectic group containing a subsystem subgroup”, J. Math. Sci. (N. Y.), 151:3 (2008), 2937–2948  crossref  elib
    2. N. Vavilov, “Geometriya 1-torov v $\mathrm{GL}_n$”, Algebra i analiz, 19:3 (2007), 119–150  mathnet  mathscinet  zmath  elib; N. Vavilov, “Geometry of 1-tori in $\mathrm{GL}(n,T)$”, St. Petersburg Math. J., 19:3 (2008), 407–429  crossref  isi
    3. N. Vavilov, “Vesovye elementy grupp Shevalle”, Algebra i analiz, 20:1 (2008), 34–85  mathnet  mathscinet  zmath  elib; N. Vavilov, “Weight elements of Chevalley groups”, St. Petersburg Math. J., 20:1 (2009), 23–57  crossref  isi
    4. N. A. Vavilov, A. A. Semenov, “Dlinnye kornevye tory v gruppakh Shevalle”, Algebra i analiz, 24:3 (2012), 22–83  mathnet  mathscinet  zmath  elib; N. A. Vavilov, A. A. Semenov, “Long root tori in Chevalley groups”, St. Petersburg Math. J., 24:3 (2013), 387–430  crossref  isi  elib
  • Записки научных семинаров ПОМИ
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