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Mat. Sb. (N.S.), 1982, Volume 117(159), Number 4, Pages 534–547 (Mi msb2234)  

This article is cited in 24 scientific papers (total in 24 papers)

Automorphisms of matrix groups over commutative ring

V. M. Petechuk


Abstract: This article contains a study of the matrix groups $E_n(R)$, $SL_n$, $SL_n'$, $GL_n$ and $GL_n'$ over an arbitrary commutative ring $R$, for $n\geqslant4$.
Bibliography: 24 titles.

Full text: PDF file (792 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1983, 45:4, 527–542

Bibliographic databases:

UDC: 512.864
MSC: 20G35, 20E36
Received: 21.04.1981

Citation: V. M. Petechuk, “Automorphisms of matrix groups over commutative ring”, Mat. Sb. (N.S.), 117(159):4 (1982), 534–547; Math. USSR-Sb., 45:4 (1983), 527–542

Citation in format AMSBIB
\Bibitem{Pet82}
\by V.~M.~Petechuk
\paper Automorphisms of matrix groups over commutative ring
\jour Mat. Sb. (N.S.)
\yr 1982
\vol 117(159)
\issue 4
\pages 534--547
\mathnet{http://mi.mathnet.ru/msb2234}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=651144}
\zmath{https://zbmath.org/?q=an:0511.20029|0496.20026}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 45
\issue 4
\pages 527--542
\crossref{https://doi.org/10.1070/SM1983v045n04ABEH001024}


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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. Michael L Bolla, “Isomorphisms of general linear groups over rings”, Journal of Algebra, 96:2 (1985), 592  crossref
    2. Vaserstein L., “Normal-Subgroups of the General Linear-Groups Over Banach-Algebras”, J. Pure Appl. Algebr., 41:1 (1986), 99–112  crossref  mathscinet  zmath  isi
    3. Stepanov A., “A Ring of Finite Stable Rank Is Not Necessarily Dedekind Finite”, 296, no. 3, 1987, 546–549  mathscinet  isi
    4. Li F., Li Z., “Isomorphisms of Gl3 Over Commutative Rings”, 31, no. 1, 1988, 7–14  mathscinet  zmath  isi
    5. Li Fuan, “Isomorphisms of Steinberg groups over commutative rings”, Acta Math Sinica, 5:2 (1989), 146  crossref  mathscinet  zmath
    6. Li Fuan, “Infinite steinberg groups”, Acta Math Sinica, 10:2 (1994), 149  crossref  mathscinet  zmath
    7. Nikolai Vavilov, Eugene Plotkin, “Chevalley groups over commutative rings: I. Elementary calculations”, Acta Appl Math, 45:1 (1996), 73  crossref  mathscinet  zmath  isi  elib
    8. Wong S., “Twists of Galois Representations and Projective Automorphisms”, J. Number Theory, 74:1 (1999), 1–18  crossref  mathscinet  zmath  isi
    9. N. A. Vavilov, V. G. Kazakevich, “Yet another variation on the theme of decomposition of transvections”, Vestnik St Petersb Univ Math, 41:4 (2008), 345  crossref  mathscinet
    10. N. A. Vavilov, V. G. Kazakevich, “Decomposition of transvections for automorphisms”, J. Math. Sci. (N. Y.), 161:4 (2009), 483–491  mathnet  crossref  zmath  elib
    11. 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
    12. E. I. Bunina, “Automorphisms of elementary adjoint Chevalley groups of types $A_l$, $D_l$, and $E_l$ over local rings with 1/2”, Algebra and Logic, 48:4 (2009), 250–267  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    13. 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  mathnet  crossref  mathscinet  elib  elib
    14. 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  mathnet  crossref  mathscinet  elib  elib
    15. E.I. Bunina, “Automorphisms of Chevalley groups of type over local rings with 1/2”, Journal of Algebra, 323:8 (2010), 2270  crossref
    16. Klyachko A.A., “Automorphisms and Isomorphisms of Chevalley Groups and Algebras”, J. Algebra, 324:10 (2010), 2608–2619  crossref  mathscinet  zmath  isi  elib
    17. 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  mathnet  crossref  mathscinet  isi  elib  elib
    18. N. A. Vavilov, A. V. Stepanov, “Linear groups over general rings. I. Generalities”, J. Math. Sci. (N. Y.), 188:5 (2013), 490–550  mathnet  crossref  mathscinet
    19. E.I. Bunina, “Automorphisms of Chevalley groups of different types over commutative rings”, Journal of Algebra, 2012  crossref
    20. A. S. Atkarskaya, “Automorphisms of stable linear groups over commutative local rings with $1/2$”, J. Math. Sci., 197:4 (2014), 455–466  mathnet  crossref
    21. E. I. Bunina, P. A. Veryovkin, “Automorphisms of Chevalley groups of type $G_2$ over local rings without $1/2$”, J. Math. Sci., 197:4 (2014), 479–491  mathnet  crossref
    22. E. I. Bunina, A. V. Mikhalev, I. O. Solovyev, “Elementary equivalence of stable linear groups over local commutative rings with $1/2$”, J. Math. Sci., 233:5 (2018), 646–655  mathnet  crossref
    23. You H., “A note on the existence of nontrivial homomorphism En(R) En1(R)”, J. Algebra. Appl., 16:1 (2017), 1750010  crossref  mathscinet  zmath  isi  scopus
    24. A. V. Litavrin, “Avtomorfizmy nekotorykh magm poryadka $k+k^2$”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 26 (2018), 47–61  mathnet  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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