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Zap. Nauchn. Sem. POMI, 2000, Volume 272, Pages 68–85 (Mi znsl1363)  

This article is cited in 14 scientific papers (total in 14 papers)

Overgroups of $\mathrm{EO}(2l,R)$

N. A. Vavilov, V. A. Petrov

Saint-Petersburg State University

Abstract: Let $R$ be a commutative ring with 1, $2\in R^*$, and $l\ge 3$. We describe subgroups of the general linear group $\mathrm{GL}(n,R)$ containing the split elementary orthogonal group $\mathrm{EO}(2l,R)$. For every intermediate subgroup $H$ there exists a unique maximal ideal $A\unlhd R$ such that $E(2l,R,A)\le H$, and moreover $H$ normalises $\mathrm{EO}(2l,R)E(2l,R,A)$. In the case when $R=K$ is a field, similar results have been obtained earlier by Dye, King, Li Shangzhi and Bashkirov.

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English version:
Journal of Mathematical Sciences (New York), 2003, 116:1, 2917–2925

Bibliographic databases:

UDC: 519.46
Received: 10.06.2000

Citation: N. A. Vavilov, V. A. Petrov, “Overgroups of $\mathrm{EO}(2l,R)$”, Problems in the theory of representations of algebras and groups. Part 7, Zap. Nauchn. Sem. POMI, 272, POMI, St. Petersburg, 2000, 68–85; J. Math. Sci. (N. Y.), 116:1 (2003), 2917–2925

Citation in format AMSBIB
\by N.~A.~Vavilov, V.~A.~Petrov
\paper Overgroups of $\mathrm{EO}(2l,R)$
\inbook Problems in the theory of representations of algebras and groups. Part~7
\serial Zap. Nauchn. Sem. POMI
\yr 2000
\vol 272
\pages 68--85
\publ POMI
\publaddr St.~Petersburg
\jour J. Math. Sci. (N. Y.)
\yr 2003
\vol 116
\issue 1
\pages 2917--2925

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    This publication is cited in the following articles:
    1. N. A. Vavilov, V. A. Petrov, “On supergroups of $\mathrm{Ep}(2l,R)$”, St. Petersburg Math. J., 15:4 (2004), 515–543  mathnet  crossref  mathscinet  zmath
    2. Petrov V., “Overgroups of unitary groups”, K–Theory, 29:3 (2003), 147–174  crossref  mathscinet  zmath  isi  scopus
    3. 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
    4. Hong You, “Overgroups of classical groups in linear group over Banach algebras”, Journal of Algebra, 304:2 (2006), 1004–1013  crossref  mathscinet  zmath  isi  scopus
    5. You H., “Overgroups of classical groups over commutative rings in linear group”, Science in China Series A–Mathematics, 49:5 (2006), 626–638  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. 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  elib  elib
    7. 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
    8. 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
    9. Xing Tao Wang, Cheng Shao Hong, “Overgroups of the elementary unitary group in linear group over commutative rings”, Journal of Algebra, 320:3 (2008), 1255–1260  crossref  mathscinet  zmath  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. 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
    12. Bakulin S.V., Vavilov N.A., “O podgruppakh, normalizuemykh $EO(2L,R)$*”, Vestnik Sankt-Peterburgskogo universiteta. Seriya 1: Matematika. Mekhanika. Astronomiya, 2011, no. 4, 19–27  mathscinet  zmath  elib
    13. 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
    14. T. N. Hoi, N. H. T. Nhat, “Subgroups of the general linear group containing the elementary subgroup over a commutative ring extension of rank 2”, Voprosy teorii predstavlenii algebr i grupp. 31, Zap. nauchn. sem. POMI, 455, POMI, SPb., 2017, 209–225  mathnet  mathscinet
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