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Zap. Nauchn. Sem. LOMI, 1979, Volume 94, Pages 21–36 (Mi znsl1801)  

This article is cited in 3 scientific papers (total in 3 papers)

Parabolic subgroups of twisted Chevalley groups over a semilocal ring

N. A. Vavilov


Abstract: It is shown that, under minor additional assumptions, the standard parabolic subgroups of a Chevalley group $G_\rho(\Phi,R)$ of twisted type $\Phi=A_\ell$, $\ell$ – odd, $D_\ell$ ,$E_6$ over a commutative semilocal ring $R$ with involution $\rho$ are in one-to-one correspondence with the $\rho$-invariant parabolic nets of ideals of $R$ of type $\Phi$, i.e., with the sets, of ideals $\sigma_\alpha$ of $R$ such that: (1) whenever; (2) $\rho\sigma_\alpha=\sigma_{\rho\alpha}$ for all $\alpha$; (3 $\sigma_\alpha=R$ for $\alpha>0$. For Chevalley groups of normal types, analogous results were obtained in Ref. Zh. Mat. 1976, 10A151; 1977, 10A 301; 1978, 6A476.

Full text: PDF file (1547 kB)

English version:
Journal of Soviet Mathematics, 1982, 19:1, 987–998

Bibliographic databases:

UDC: 513.6

Citation: N. A. Vavilov, “Parabolic subgroups of twisted Chevalley groups over a semilocal ring”, Rings and modules. Part 2, Zap. Nauchn. Sem. LOMI, 94, "Nauka", Leningrad. Otdel., Leningrad, 1979, 21–36; J. Soviet Math., 19:1 (1982), 987–998

Citation in format AMSBIB
\Bibitem{Vav79}
\by N.~A.~Vavilov
\paper Parabolic subgroups of twisted Chevalley groups over a semilocal ring
\inbook Rings and modules. Part~2
\serial Zap. Nauchn. Sem. LOMI
\yr 1979
\vol 94
\pages 21--36
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl1801}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=571512}
\zmath{https://zbmath.org/?q=an:0485.20038|0445.20027}
\transl
\jour J. Soviet Math.
\yr 1982
\vol 19
\issue 1
\pages 987--998
\crossref{https://doi.org/10.1007/BF01476110}


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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. N. A. Vavilov, “On subgroups of the unitary group over a semilocal ring”, Russian Math. Surveys, 37:4 (1982), 145–146  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. V. Alexandrov, N. A. Vavilov, “Parabolic subgroups of $\mathrm{SL}_n$ and $\mathrm{Sp}_{2l}$ over a Dedekind ring of arithmetic type”, J. Math. Sci. (N. Y.), 171:3 (2010), 307–316  mathnet  crossref
    3. K. O. Batalkin, N. A. Vavilov, “Parabolicheskie podgruppy $\mathrm{SO}_{2l}$ nad dedekindovym koltsom arifmeticheskogo tipa”, Voprosy teorii predstavlenii algebr i grupp. 23, Zap. nauchn. sem. POMI, 400, POMI, SPb., 2012, 50–69  mathnet  mathscinet; K. O. Batalkin, N. A. Vavilov, “Parabolic subgroups of $\mathrm{SO}_{2l}$ over a Dedekind ring of arithmetic type”, J. Math. Sci. (N. Y.), 192:2 (2013), 154–163  crossref
  • Записки научных семинаров ПОМИ
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