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Algebra i Analiz, 2004, Volume 16, Issue 4, Pages 54–87 (Mi aa619)  

This article is cited in 42 scientific papers (total in 43 papers)

Research Papers

An A2-proof of structure theorems for Chevalley groups of types E6 and E7

N. A. Vavilova, M. R. Gavrilovichb

a St. Petersburg State University, Department of Mathematics and Mechanics
b University of Oxford
References:
Received: 25.06.2003
English version:
St. Petersburg Mathematical Journal, 2005, Volume 16, Issue 4, Pages 649–672
DOI: https://doi.org/10.1090/S1061-0022-05-00871-X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: N. A. Vavilov, M. R. Gavrilovich, “An A2-proof of structure theorems for Chevalley groups of types E6 and E7”, Algebra i Analiz, 16:4 (2004), 54–87; St. Petersburg Math. J., 16:4 (2005), 649–672
Citation in format AMSBIB
\Bibitem{VavGav04}
\by N.~A.~Vavilov, M.~R.~Gavrilovich
\paper An $\mathrm{A}_2$-proof of structure theorems for Chevalley groups of types $\mathrm{E}_6$ and $\mathrm{E}_7$
\jour Algebra i Analiz
\yr 2004
\vol 16
\issue 4
\pages 54--87
\mathnet{http://mi.mathnet.ru/aa619}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2090851}
\zmath{https://zbmath.org/?q=an:1105.20039}
\transl
\jour St. Petersburg Math. J.
\yr 2005
\vol 16
\issue 4
\pages 649--672
\crossref{https://doi.org/10.1090/S1061-0022-05-00871-X}
Linking options:
  • https://www.mathnet.ru/eng/aa619
  • https://www.mathnet.ru/eng/aa/v16/i4/p54
  • This publication is cited in the following 43 articles:
    1. Andrei Jaikin-Zapirain, Steffen Kionke, “Asymptotic invariants of residually finite just infinite groups”, European Journal of Mathematics, 11:1 (2025)  crossref
    2. E. B. Plotkin, A. I. Generalov, N. S. Geldkhauzer, N. L. Gordeev, A. Yu. Luzgarev, V. V. Nesterov, I. A. Panin, V. A. Petrov, S. Yu. Pilyugin, A. V. Stepanov, A. K. Stavrova, V. G. Khalin, “O Nikolae Aleksandroviche Vavilove”, Voprosy teorii predstavlenii algebr i grupp. 40, Posvyaschaetsya pamyati Nikolaya Aleksandrovicha VAVILOVA, Zap. nauchn. sem. POMI, 531, POMI, SPb., 2024, 7–40  mathnet
    3. N. A. Vavilov, Z. Zhang, “Relative Centralizers of Relative Subgroups”, J Math Sci, 264:1 (2022), 4  crossref
    4. P. B. Gvozdevskiy, “Overgroups of subsystem subgroups in exceptional groups: nonideal levels”, St. Petersburg Math. J., 33:6 (2022), 897–925  mathnet  crossref
    5. N. A. Vavilov, Z. Zhang, “Relative centralisers of relative subgroups”, Voprosy teorii predstavlenii algebr i grupp. 35, Zap. nauchn. sem. POMI, 492, POMI, SPb., 2020, 10–24  mathnet
    6. P. B. Gvozdevskiǐ, “Overgroups of subsystem subgroups in exceptional groups: $2A_1$-proof”, St. Petersburg Math. J., 32:6 (2021), 1011–1031  mathnet  crossref
    7. P. B. Gvozdevsky, “Overgroups of Levi subgroups I. The case of abelian unipotent radical”, St. Petersburg Math. J., 31:6 (2020), 969–999  mathnet  crossref  isi  elib
    8. Preusser R., “Sandwich Classification For O2N+1(R) and U2N+1(R, Delta) Revisited”, J. Group Theory, 21:4 (2018), 539–571  crossref  mathscinet  zmath  isi  scopus
    9. J. Math. Sci. (N. Y.), 243:4 (2019), 515–526  mathnet  crossref
    10. Raimund Preusser, “Sandwich classification for GL n (R), O2n (R) and U2n (R,Λ) revisited”, Journal of Group Theory, 21:1 (2018), 21  crossref
    11. V. A. Petrov, “Decomposition of transvections: an algebro-geometric approach”, St. Petersburg Math. J., 28:1 (2017), 109–114  mathnet  crossref  mathscinet  isi  elib
    12. J. Math. Sci. (N. Y.), 209:6 (2015), 922–934  mathnet  crossref
    13. J. Math. Sci. (N. Y.), 219:3 (2016), 355–369  mathnet  crossref  mathscinet
    14. Hazrat R. Vavilov N. Zhang Z., “Relative Commutator Calculus in Chevalley Groups”, J. Algebra, 385 (2013), 262–293  crossref  mathscinet  zmath  isi  elib  scopus
    15. Bardini C., “Standardness and Standard Automorphisms of Chevalley Groups, I: the Case of Rank at Least Two”, Chin. Ann. Math. Ser. B, 33:5 (2012), 783–800  crossref  mathscinet  zmath  isi  elib  scopus
    16. N. A. Vavilov, A. V. Shchegolev, “Overgroups of subsystem subgroups in exceptional groups: levels”, J. Math. Sci. (N. Y.), 192:2 (2013), 164–195  mathnet  crossref  mathscinet
    17. N. A. Vavilov, A. Yu. Luzgarev, “Chevalley group of type $\mathrm E_7$ in the 56-dimensional representation”, J. Math. Sci. (N. Y.), 180:3 (2012), 197–251  mathnet  crossref
    18. I. M. Pevzner, “Width of groups of type $\mathrm E_6$ with respect to root elements. II”, J. Math. Sci. (N. Y.), 180:3 (2012), 338–350  mathnet  crossref
    19. I. M. Pevzner, “The geometry of root elements in groups of type $\mathrm E_6$”, St. Petersburg Math. J., 23:3 (2012), 603–635  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    20. I. M. Pevzner, “Width of groups of type $\mathrm E_6$ with respect to root elements. I”, St. Petersburg Math. J., 23:5 (2012), 891–919  mathnet  crossref  mathscinet  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
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