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Zap. Nauchn. Sem. LOMI, 1982, Volume 116, Pages 20–43 (Mi znsl1748)  

This article is cited in 9 scientific papers (total in 9 papers)

Parabolic subgroups of Chevalley groups over a commutative ring

N. A. Vavilov


Abstract: This is a survey of results describing the parabolic subgroups of Chevalley groups over rings of various types. For Chevalley groups of classical types over an arbitrary commutative ring, a description of parabolic subgroups is obtained which may be considered definitive. Some errors in the results of V. M. Levchuk in Mat. Zametki, Volume 31, No. 4 (1982) are pointed out.

Full text: PDF file (2641 kB)

English version:
Journal of Soviet Mathematics, 1984, 26:3, 1848–1860

Bibliographic databases:

UDC: 513.6, 519.46

Citation: N. A. Vavilov, “Parabolic subgroups of Chevalley groups over a commutative ring”, Integral lattices and finite linear groups, Zap. Nauchn. Sem. LOMI, 116, "Nauka", Leningrad. Otdel., Leningrad, 1982, 20–43; J. Soviet Math., 26:3 (1984), 1848–1860

Citation in format AMSBIB
\Bibitem{Vav82}
\by N.~A.~Vavilov
\paper Parabolic subgroups of Chevalley groups over a commutative ring
\inbook Integral lattices and finite linear groups
\serial Zap. Nauchn. Sem. LOMI
\yr 1982
\vol 116
\pages 20--43
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl1748}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=687837}
\zmath{https://zbmath.org/?q=an:0539.20024|0513.20029}
\transl
\jour J. Soviet Math.
\yr 1984
\vol 26
\issue 3
\pages 1848--1860
\crossref{https://doi.org/10.1007/BF01670569}


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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, M. R. Gavrilovich, “$\mathrm A_2$-dokazatelstvo strukturnykh teorem dlya grupp Shevalle tipov $\mathrm E_6$ i $\mathrm E_7$”, Algebra i analiz, 16:4 (2004), 54–87  mathnet  mathscinet  zmath; N. A. Vavilov, M. R. Gavrilovich, “$\mathrm A_2$-proof of structure theorem for Chevaller groups of type $\mathrm E_6$ and $\mathrm E_7$”, St. Petersburg Math. J., 16:4 (2005), 649–672  crossref
    2. K. Yu. Lavrov, “Podgruppy ortogonalnykh grupp chetnogo poryadka nad lokalnym polem”, Voprosy teorii predstavlenii algebr i grupp. 12, Zap. nauchn. sem. POMI, 321, POMI, SPb., 2005, 240–250  mathnet  mathscinet  zmath; K. Yu. Lavrov, “Subgroups of the orthogonal groups of even degree over a local field”, J. Math. Sci. (N. Y.), 136:3 (2006), 3966–3971  crossref
    3. E. I. Bunina, “Avtomorfizmy grupp Shevalle tipa $B_l$ nad lokalnymi koltsami s 1/2”, Fundament. i prikl. matem., 15:7 (2009), 3–46  mathnet  mathscinet  elib; E. I. Bunina, “Automorphisms of Chevalley groups of type $B_l$ over local rings with 1/2”, J. Math. Sci., 169:5 (2010), 557–588  crossref  elib
    4. E. I. Bunina, “Avtomorfizmy grupp Shevalle tipov $A_l$, $D_l$, $E_l$ nad lokalnymi koltsami s neobratimoi dvoikoi”, Fundament. i prikl. matem., 15:7 (2009), 47–80  mathnet  mathscinet  elib; E. I. Bunina, “Automorphisms of Chevalley groups of types $A_l$, $D_l$, $E_l$ over local rings without 1/2”, J. Math. Sci., 169:5 (2010), 589–613  crossref  elib
    5. 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
    6. N. A. Vavilov, S. S. Sinchuk, “Dennis–Vaserstein type decompositions”, J. Math. Sci. (N. Y.), 171:3 (2010), 331–337  mathnet  crossref
    7. N. A. Vavilov, A. V. Smolenskii, B. Suri, “Unitreugolnye faktorizatsii grupp Shevalle”, Voprosy teorii predstavlenii algebr i grupp. 21, Zap. nauchn. sem. POMI, 388, POMI, SPb., 2011, 17–47  mathnet; N. A. Vavilov, A. V. Smolensky, B. Sury, “Unitriangular factorisations of Chevalley groups”, J. Math. Sci. (N. Y.), 183:5 (2012), 584–599  crossref
    8. N. A. Vavilov, S. S. Sinchuk, “Parabolicheskie faktorizatsii rasschepimykh klassicheskikh grupp”, Algebra i analiz, 23:4 (2011), 1–30  mathnet  mathscinet  zmath  elib; N. A. Vavilov, S. S. Sinchuk, “Parabolic factorizations of split classical groups”, St. Petersburg Math. J., 23:4 (2012), 637–657  crossref  isi  elib
    9. 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
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