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Trudy Mat. Inst. Steklov., 1984, Volume 165, Pages 24–42 (Mi tm2269)  

This article is cited in 18 scientific papers (total in 18 papers)

Arrangement of subgroups in the general linear group over a commutative ring

Z. I. Borevich, N. A. Vavilov


Full text: PDF file (2215 kB)

English version:
Proceedings of the Steklov Institute of Mathematics, 1985, 165, 27–46

Bibliographic databases:

UDC: 512.547

Citation: Z. I. Borevich, N. A. Vavilov, “Arrangement of subgroups in the general linear group over a commutative ring”, Algebraic geometry and its applications, Collection of articles, Trudy Mat. Inst. Steklov., 165, 1984, 24–42; Proc. Steklov Inst. Math., 165 (1985), 27–46

Citation in format AMSBIB
\Bibitem{BorVav84}
\by Z.~I.~Borevich, N.~A.~Vavilov
\paper Arrangement of subgroups in the general linear group over a~commutative ring
\inbook Algebraic geometry and its applications
\bookinfo Collection of articles
\serial Trudy Mat. Inst. Steklov.
\yr 1984
\vol 165
\pages 24--42
\mathnet{http://mi.mathnet.ru/tm2269}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=752930}
\zmath{https://zbmath.org/?q=an:0653.20048}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1985
\vol 165
\pages 27--46


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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. I. Z. Golubchik, “O polnoi lineinoi gruppe nad slabo neterovymi assotsiativnymi algebrami”, Fundament. i prikl. matem., 1:3 (1995), 661–668  mathnet  mathscinet  zmath
    2. A. V. Stepanov, “O normalnom stroenii polnoi lineinoi gruppy nad koltsom”, Voprosy teorii predstavlenii algebr i grupp. 5, Zap. nauchn. sem. POMI, 236, POMI, SPb., 1997, 166–182  mathnet  mathscinet  zmath; A. V. Stepanov, “On the normal structure of the general linear group over a ring”, J. Math. Sci. (New York), 95:2 (1999), 2146–2155  crossref
    3. N. A. Vavilov, V. A. Petrov, “O nadgruppakh $\mathrm{Ep}(2l,R)$”, Algebra i analiz, 15:4 (2003), 72–114  mathnet  mathscinet  zmath; N. A. Vavilov, V. A. Petrov, “On supergroups of $\mathrm{Ep}(2l,R)$”, St. Petersburg Math. J., 15:4 (2004), 515–543  crossref
    4. 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
    5. E. V. Dybkova, “Nadgruppy diagonalnoi gruppy v giperbolicheskoi unitarnoi gruppe nad prostym artinovym koltsom. I”, Voprosy teorii predstavlenii algebr i grupp. 14, Zap. nauchn. sem. POMI, 338, POMI, SPb., 2006, 155–172  mathnet  mathscinet  zmath; E. V. Dybkova, “Overgroups of the diagonal group in the hyperbolic unitary group over a simple Artin ring”, J. Math. Sci. (N. Y.), 145:1 (2007), 4781–4789  crossref
    6. N. A. Vavilov, M. R. Gavrilovich, S. I. Nikolenko, “Stroenie grupp Shevalle: Dokazatelstvo iz Knigi”, Voprosy teorii predstavlenii algebr i grupp. 13, Zap. nauchn. sem. POMI, 330, POMI, SPb., 2006, 36–76  mathnet  mathscinet  zmath  elib; N. A. Vavilov, M. R. Gavrilovich, S. I. Nikolenko, “Structure of Chevalley groups: the proof from the Book”, J. Math. Sci. (N. Y.), 140:5 (2007), 626–645  crossref  elib
    7. N. A. Vavilov, V. A. Petrov, “O nadgruppakh $\mathrm{EO}(n,R)$”, Algebra i analiz, 19:2 (2007), 10–51  mathnet  mathscinet  zmath  elib; N. A. Vavilov, V. A. Petrov, “Overgroups of $\mathrm{EO}(n,R)$”, St. Petersburg Math. J., 19:2 (2008), 167–195  crossref  isi
    8. 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
    9. N. A. Vavilov, S. I. Nikolenko, “$\mathrm A_2$-dokazatelstvo strukturnykh teorem dlya gruppy Shevalle tipa $\mathrm F_4$”, Algebra i analiz, 20:4 (2008), 27–63  mathnet  mathscinet  zmath  elib; N. A. Vavilov, S. I. Nikolenko, “$\mathrm A_2$-proof of structure theorems for Chevalley groups of type $\mathrm F_4$”, St. Petersburg Math. J., 20:4 (2009), 527–551  crossref  isi
    10. A. S. Ananievskiy, N. A. Vavilov, S. S. Sinchuk, “Overgroups of $E(m,R)\otimes E(n,R)$”, J. Math. Sci. (N. Y.), 161:4 (2009), 461–473  mathnet  crossref  elib
    11. N. A. Vavilov, V. G. Kazakevich, “More variations on decomposition of transvections”, J. Math. Sci. (N. Y.), 171:3 (2010), 322–330  mathnet  crossref
    12. A. S. Ananevskii, N. A. Vavilov, S. S. Sinchuk, “O nadgruppakh $E(m,R)\otimes E(n,R)$. I. Urovni i normalizatory”, Algebra i analiz, 23:5 (2011), 55–98  mathnet  mathscinet  elib; A. S. Ananyevskiy, N. A. Vavilov, S. S. Sinchuk, “Overgroups of $E(m,R)\otimes E(n,R)$. I”, St. Petersburg Math. J., 23:5 (2012), 819–849  crossref  isi  elib
    13. N. A. Vavilov, A. V. Stepanov, “Lineinye gruppy nad obschimi koltsami I. Obschie mesta”, Voprosy teorii predstavlenii algebr i grupp. 22, Zap. nauchn. sem. POMI, 394, POMI, SPb., 2011, 33–139  mathnet  mathscinet; N. A. Vavilov, A. V. Stepanov, “Linear groups over general rings. I. Generalities”, J. Math. Sci. (N. Y.), 188:5 (2013), 490–550  crossref
    14. Bakulin S.V., Vavilov N.A., Vestnik Sankt-Peterburgskogo universiteta. Seriya 1: Matematika. Mekhanika. Astronomiya, 2011, no. 4, 19–27  elib
    15. N. A. Vavilov, A. V. Schegolev, “Nadgruppy subsystem subgroups v isklyuchitelnykh gruppakh: urovni”, Voprosy teorii predstavlenii algebr i grupp. 23, Zap. nauchn. sem. POMI, 400, POMI, SPb., 2012, 70–126  mathnet  mathscinet; N. A. Vavilov, A. V. Shchegolev, “Overgroups of subsystem subgroups in exceptional groups: levels”, J. Math. Sci. (N. Y.), 192:2 (2013), 164–195  crossref
    16. A. V. Stepanov, “Neabeleva $K$-teoriya grupp Shevalle nad koltsami”, Voprosy teorii predstavlenii algebr i grupp. 26, Zap. nauchn. sem. POMI, 423, POMI, SPb., 2014, 244–263  mathnet  mathscinet; A. V. Stepanov, “Non-Abelian $K$-theory for Chevalley groups over rings”, J. Math. Sci. (N. Y.), 209:4 (2015), 645–656  crossref
    17. A. V. Stepanov, “Novyi vzglyad na razlozhenie unipotentov i normalnoe stroenie grupp Shevalle”, Algebra i analiz, 28:3 (2016), 161–173  mathnet  mathscinet  elib; A. V. Stepanov, “A new look at the decomposition of unipotents and the normal structure of Chevalley groups”, St. Petersburg Math. J., 28:3 (2017), 411–419  crossref  isi
    18. 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
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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