A. Yu. Luzgarev, “Overgroups of $\mathrm{F}_4$ in $\mathrm{E}_6$ over commutative rings”, Algebra i Analiz, 20:6 (2008), 148–185; St. Petersburg Math. J., 20:6 (2009), 955

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Algebra i Analiz, 2008, Volume 20, Issue 6, Pages 148–185 (Mi aa543)

This article is cited in 21 scientific papers (total in 22 papers)

Research Papers

Overgroups of

F_{4}

$\mathrm{F}_4$ in

E_{6}

$\mathrm{E}_6$ over commutative rings

A. Yu. Luzgarev

St. Petersburg State University, Department of Mathematics and Mechanics

Full-text PDF (446 kB) Citations (22)

References:

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Abstract: Overgroups of the elementary Chevalley group of type

F_{4}

$\mathrm F_4$ in the Chevalley group of type

E_{6}

$\mathrm E_6$ over an arbitrary commutative ring are described.

Keywords: Chevalley group, exceptional groups over commutative rings, localization-completion method.

Received: 12.02.2008

English version:
St. Petersburg Mathematical Journal, 2009, Volume 20, Issue 6, Pages 955–981
DOI: https://doi.org/10.1090/S1061-0022-09-01080-2

Bibliographic databases:

Document Type: Article

MSC: 20H25

Language: Russian

Citation: A. Yu. Luzgarev, “Overgroups of

F_{4}

$\mathrm{F}_4$ in

E_{6}

$\mathrm{E}_6$ over commutative rings”, Algebra i Analiz, 20:6 (2008), 148–185; St. Petersburg Math. J., 20:6 (2009), 955–981

Citation in format AMSBIB

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\transl

\jour St. Petersburg Math. J.

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\pages 955--981

\crossref{https://doi.org/10.1090/S1061-0022-09-01080-2}

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Linking options:

https://www.mathnet.ru/eng/aa543

https://www.mathnet.ru/eng/aa/v20/i6/p148

This publication is cited in the following 22 articles:

Roman Lubkov, Ilia Nekrasov, “Overgroups of exterior powers of an elementary group. levels”, Linear and Multilinear Algebra, 72:4 (2024), 563
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
R. Lubkov, A. Stepanov, “Subgroups of Chevalley Groups Over Rings”, J Math Sci, 252:6 (2021), 829
P. B. Gvozdevskiy, “Overgroups of subsystem subgroups in exceptional groups: nonideal levels”, St. Petersburg Math. J., 33:6 (2022), 897–925
P. B. Gvozdevskiǐ, “Overgroups of subsystem subgroups in exceptional groups: $2A_1$-proof”, St. Petersburg Math. J., 32:6 (2021), 1011–1031
R. Lubkov, A. Stepanov, “Subgroups of Chevalley groups over rings”, Voprosy teorii predstavlenii algebr i grupp. 35, Zap. nauchn. sem. POMI, 484, POMI, SPb., 2019, 121–137
J. Math. Sci. (N. Y.), 222:4 (2017), 466–515
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
J. Math. Sci. (N. Y.), 200:6 (2014), 742–768
Hazrat R., Vavilov N., Zhang Z., “Relative Commutator Calculus in Chevalley Groups”, J. Algebra, 385 (2013), 262–293
N. A. Vavilov, A. V. Shchegolev, “Overgroups of subsystem subgroups in exceptional groups: levels”, J. Math. Sci. (N. Y.), 192:2 (2013), 164–195
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
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
J. Math. Sci. (N. Y.), 179:6 (2011), 662–678
I. M. Pevzner, “The geometry of root elements in groups of type $\mathrm E_6$”, St. Petersburg Math. J., 23:3 (2012), 603–635
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
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
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
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
N. A. Vavilov, “Stroenie izotropnykh reduktivnykh grupp”, Tr. In-ta matem., 18:1 (2010), 15–27

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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