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

This article is cited in 34 scientific papers (total in 34 papers)

Research Papers

$\mathrm A_2$-proof of structure theorem for Chevaller groups of type $\mathrm E_6$ and $\mathrm E_7$

N. A. Vavilova, M. R. Gavrilovichb

a St. Petersburg State University, Department of Mathematics and Mechanics
b University of Oxford

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English version:
St. Petersburg Mathematical Journal, 2005, 16:4, 649–672

Bibliographic databases:

Received: 25.06.2003

Citation: N. A. Vavilov, M. R. Gavrilovich, “$\mathrm A_2$-proof of structure theorem for Chevaller groups of type $\mathrm E_6$ and $\mathrm E_7$”, 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 $\mathrm A_2$-proof of structure theorem for Chevaller groups of type $\mathrm E_6$ 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://www.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}


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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. A. Yu. Luzgarev, “On overgroups of $\mathrm{E}(\mathrm{E}_6,R)$ and $\mathrm{E}(\mathrm{E}_7,R)$ in their minimal representations”, J. Math. Sci. (N. Y.), 134:6 (2006), 2558–2571  mathnet  crossref  mathscinet  zmath  scopus
    2. N. A. Vavilov, A. Yu. Luzgarev, I. M. Pevzner, “Chevalley group of type $\mathrm E_6$ in the 27-dimensional representation”, J. Math. Sci. (N. Y.), 145:1 (2007), 4697–4736  mathnet  crossref  mathscinet  zmath  elib  elib  scopus
    3. 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  mathnet  crossref  mathscinet  zmath  elib  elib  scopus
    4. N. A. Vavilov, A. K. Stavrova, “Basic reductions for the description of normal subgroups”, J. Math. Sci. (N. Y.), 151:3 (2008), 2949–2960  mathnet  crossref  mathscinet  zmath  elib  elib  scopus
    5. N. A. Vavilov, V. A. Petrov, “Overgroups of $\mathrm{EO}(n,R)$”, St. Petersburg Math. J., 19:2 (2008), 167–195  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    6. N. A. Vavilov, “Can one see the signs of structure constants?”, St. Petersburg Math. J., 19:4 (2008), 519–543  mathnet  crossref  mathscinet  zmath  isi  scopus
    7. N. A. Vavilov, A. Yu. Luzgarev, “The normalizer of Chevalley groups of type $\mathrm{E}_6$”, St. Petersburg Math. J., 19:5 (2008), 699–718  mathnet  crossref  mathscinet  zmath  isi  scopus
    8. N. A. Vavilov, “On subgroups of symplectic group containing a subsystem subgroup”, J. Math. Sci. (N. Y.), 151:3 (2008), 2937–2948  mathnet  crossref  mathscinet  zmath  elib  elib  scopus
    9. Vavilov N., “An $A_3$-proof of structure theorems for Chevalley groups of types $E_6$ and $E_7$”, Internat. J. Algebra Comput., 17:5-6 (2007), 1283–1298  crossref  mathscinet  zmath  isi  elib
    10. 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  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    11. A. Yu. Luzgarev, “Overgroups of $\mathrm{F}_4$ in $\mathrm{E}_6$ over commutative rings”, St. Petersburg Math. J., 20:6 (2009), 955–981  mathnet  crossref  mathscinet  zmath  isi  scopus
    12. N. A. Vavilov, “Numerology of square equations”, St. Petersburg Math. J., 20:5 (2009), 687–707  mathnet  crossref  mathscinet  zmath  isi  scopus
    13. Vavilov N.A., Stepanov A.V., “Nadgruppy poluprostykh grupp”, Vestn. Samarskogo gos. un-ta. Estestvennonauchn. ser., 2008, no. 3, 51–95  mathscinet  zmath
    14. Hazrat R., Vavilov N., “Bak's work on the $K$-theory of rings”, J. K-Theory, 4:1 (2009), 1–65  crossref  mathscinet  zmath  isi  elib  scopus
    15. Stavrova A,, “Normal structure of maximal parabolic subgroups in Chevalley groups over rings”, Algebra Colloq., 16:4 (2009), 631–648  crossref  mathscinet  zmath  isi  elib  scopus
    16. J. Math. Sci. (N. Y.), 168:3 (2010), 334–348  mathnet  crossref  mathscinet  zmath  scopus
    17. 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  zmath  elib  elib  scopus
    18. 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  zmath  elib  elib  scopus
    19. N. A. Vavilov, V. G. Kazakevich, “More variations on decomposition of transvections”, J. Math. Sci. (N. Y.), 171:3 (2010), 322–330  mathnet  crossref  mathscinet  zmath  scopus
    20. Hazrat R., Petrov V., Vavilov N., “Relative subgroups in Chevalley groups”, Journal of K-Theory, 5:3 (2010), 603–618  crossref  mathscinet  zmath  isi  scopus
    21. N. A. Vavilov, “Stroenie izotropnykh reduktivnykh grupp”, Tr. In-ta matem., 18:1 (2010), 15–27  mathnet
    22. 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  mathscinet  mathscinet  zmath  scopus
    23. 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  mathscinet  zmath  scopus
    24. 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  zmath  isi  elib  elib  scopus
    25. 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  zmath  isi  elib  elib  scopus
    26. N. A. Vavilov, “An $\mathrm A_3$-proof of the structure theorems for Chevalley groups of types $\mathrm E_6$ and $\mathrm E_7$. II. The main lemma”, St. Petersburg Math. J., 23:6 (2012), 921–942  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    27. 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  zmath  scopus
    28. 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
    29. 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  zmath  scopus
    30. Hazrat R. Vavilov N. Zhang Z., “Relative Commutator Calculus in Chevalley Groups”, J. Algebra, 385 (2013), 262–293  crossref  mathscinet  zmath  isi  elib  scopus
    31. J. Math. Sci. (N. Y.), 219:3 (2016), 355–369  mathnet  crossref  mathscinet  zmath  scopus
    32. J. Math. Sci. (N. Y.), 209:6 (2015), 922–934  mathnet  crossref  mathscinet  zmath  scopus
    33. V. A. Petrov, “Decomposition of transvections: an algebro-geometric approach”, St. Petersburg Math. J., 28:1 (2017), 109–114  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    34. 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
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