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Algebra i Analiz, 2003, Volume 15, Issue 4, Pages 72–114 (Mi aa801)  

This article is cited in 33 scientific papers (total in 33 papers)

Research Papers

On supergroups of $\mathrm{Ep}(2l,R)$

N. A. Vavilov, V. A. Petrov

Saint-Petersburg State University

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English version:
St. Petersburg Mathematical Journal, 2004, 15:4, 515–543

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Received: 18.02.2003

Citation: N. A. Vavilov, V. A. Petrov, “On supergroups of $\mathrm{Ep}(2l,R)$”, Algebra i Analiz, 15:4 (2003), 72–114; St. Petersburg Math. J., 15:4 (2004), 515–543

Citation in format AMSBIB
\by N.~A.~Vavilov, V.~A.~Petrov
\paper On supergroups of $\mathrm{Ep}(2l,R)$
\jour Algebra i Analiz
\yr 2003
\vol 15
\issue 4
\pages 72--114
\jour St. Petersburg Math. J.
\yr 2004
\vol 15
\issue 4
\pages 515--543

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    This publication is cited in the following articles:
    1. Petrov V., “Overgroups of unitary groups”, $K$-Theory, 29:3 (2003), 147–174  crossref  mathscinet  zmath  isi
    2. A. Yu. Luzgarev, “O nadgruppakh $\mathrm{E}(\mathrm{E}_6,R)$ i $\mathrm{E}(\mathrm{E}_7,R)$ v minimalnykh predstavleniyakh”, Voprosy teorii predstavlenii algebr i grupp. 11, Zap. nauchn. sem. POMI, 319, POMI, SPb., 2004, 216–243  mathnet  mathscinet  zmath; 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  crossref
    3. “Overgroups of classical groups in linear group over Banach algebras”, J. Algebra, 304:2 (2006), 1004–1013  crossref  mathscinet  zmath  isi  elib
    4. You Hong, “Overgroups of classical groups over commutative rings in linear group”, Sci. China Ser. A, 49:5 (2006), 626–638  crossref  mathscinet  zmath  isi  elib
    5. N. A. Vavilov, “Subgroups of $\operatorname{SL}_n$ over a semilocal ring”, J. Math. Sci. (N. Y.), 147:5 (2007), 6995–7004  mathnet  crossref  mathscinet  elib  elib
    6. 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
    7. N. A. Vavilov, A. Yu. Luzgarev, “Normalizator gruppy Shevalle tipa $\mathrm{E}_6$”, Algebra i analiz, 19:5 (2007), 37–64  mathnet  mathscinet  zmath; 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  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. 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. A. Yu. Luzgarëv, “Opisanie nadgrupp $\mathrm F_4$ v $\mathrm E_6$ nad kommutativnym koltsom”, Algebra i analiz, 20:6 (2008), 148–185  mathnet  mathscinet  zmath; A. Yu. Luzgarev, “Overgroups of $\mathrm{F}_4$ in $\mathrm{E}_6$ over commutative rings”, St. Petersburg Math. J., 20:6 (2009), 955–981  crossref  isi
    11. Xing Tao Wang, Cheng Shao Hong, “Overgroups of the elementary unitary group in linear group over commutative rings”, J. Algebra, 320:3 (2008), 1255–1260  crossref  mathscinet  zmath  isi
    12. Vavilov N.A., Stepanov A.V., “Nadgruppy poluprostykh grupp”, Vestn. Samarskogo gos. un-ta. Estestvennonauchn. ser., 2008, no. 3, 51–95  mathscinet  zmath
    13. 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
    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
    15. 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
    16. 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
    17. 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
    18. N. A. Vavilov, V. G. Kazakevich, “More variations on decomposition of transvections”, J. Math. Sci. (N. Y.), 171:3 (2010), 322–330  mathnet  crossref
    19. J. Math. Sci. (N. Y.), 179:6 (2011), 662–678  mathnet  crossref
    20. 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
    21. 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
    22. Bashkirov E.L., “Linear groups of degree four containing the subgroup $\mathrm{SL}_2(k)\otimes\mathrm{SL}_2(k)$”, J. Pure Appl. Algebra, 215:7 (2011), 1688–1701  crossref  mathscinet  zmath  isi  elib
    23. Bakulin S.V., Vavilov N.A., “O podgruppakh, normalizuemykh $\mathrm{EO}(2L,R)$”, Vestn. Sankt-Peterburgskogo un-ta. Ser. 1. Matem. Mekh. Astronom., 2011, no. 4, 19–27  mathscinet  zmath  elib
    24. Stepanov A., “Subring Subgroups in Chevalley Groups with Doubly Laced Root Systems”, J. Algebra, 362 (2012), 12–29  crossref  mathscinet  zmath  isi  elib
    25. 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
    26. Hazrat R. Vavilov N. Zhang Z., “Relative Commutator Calculus in Chevalley Groups”, J. Algebra, 385 (2013), 262–293  crossref  mathscinet  zmath  isi  elib
    27. J. Math. Sci. (N. Y.), 200:6 (2014), 742–768  mathnet  crossref
    28. Bashkirov E.L., Gupta C.K., “Linear Groups Over Integral Extensions of Semilocal Commutative Rings”, Commun. Algebr., 42:10 (2014), 4149–4171  crossref  mathscinet  zmath  isi  elib
    29. N. A. Vavilov, A. Yu. Luzgarev, “Normalizator gruppy Shevalle tipa $\mathrm E_7$”, Algebra i analiz, 27:6 (2015), 57–88  mathnet  mathscinet  elib; N. A. Vavilov, A. Yu. Luzgarev, “Normaliser of the Chevalley group of type $\mathrm E_7$”, St. Petersburg Math. J., 27:6 (2016), 899–921  crossref  isi
    30. E. Yu. Voronetskii, “O normalnosti elementarnoi podgruppy v $\operatorname{Sp}(2, A)$”, Voprosy teorii predstavlenii algebr i grupp. 29, Zap. nauchn. sem. POMI, 443, POMI, SPb., 2016, 33–45  mathnet  mathscinet; E. Yu. Voronetsky, “Normality of elementary subgroup in $\operatorname{Sp}(2,A)$”, J. Math. Sci. (N. Y.), 222:4 (2017), 386–393  crossref
    31. R. Hazrat, N. Vavilov, Z. Zhang, “The commutators of classical groups”, Voprosy teorii predstavlenii algebr i grupp. 29, Zap. nauchn. sem. POMI, 443, POMI, SPb., 2016, 151–221  mathnet  mathscinet; J. Math. Sci. (N. Y.), 222:4 (2017), 466–515  crossref
    32. E. Yu. Voronetskii, “Normalizatory elementarnykh nadgrupp $\mathrm{Ep}(2,A)$”, Voprosy teorii predstavlenii algebr i grupp. 30, Zap. nauchn. sem. POMI, 452, POMI, SPb., 2016, 32–51  mathnet  mathscinet
    33. N. H. T. Nhat, T. N. Hoi, “The normalizer of the elementary linear group of a module arising under extension of the base ring”, Voprosy teorii predstavlenii algebr i grupp. 31, Zap. nauchn. sem. POMI, 455, POMI, SPb., 2017, 122–129  mathnet
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