M. A. Vsemirnov, “On (2,3)-generation of matrix groups over the ring of integers”, Algebra i Analiz, 19:6 (2007), 22–58; St. Petersburg Math. J., 19:6 (2008), 883

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Algebra i Analiz, 2007, Volume 19, Issue 6, Pages 22–58 (Mi aa145)

This article is cited in 10 scientific papers (total in 10 papers)

Research Papers

On (2,3)-generation of matrix groups over the ring of integers

M. A. Vsemirnov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Full-text PDF (361 kB) Citations (10)

References:

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Abstract: The groups

$\mathrm{GL}(5,\mathbb{Z})$ ,

$\mathrm{SL}(5,\mathbb{Z})$ ,

$\mathrm{SL}(6,\mathbb{Z})$ ,

$\mathrm{GL}(7,\mathbb{Z})$ and

$\mathrm{SL}(7,\mathbb{Z})$ are (2,3)-generated.

Keywords: (2,3)-generation, linear groups.

Received: 10.08.2007

English version:
St. Petersburg Mathematical Journal, 2008, Volume 19, Issue 6, Pages 883–910
DOI: https://doi.org/10.1090/S1061-0022-08-01026-1

Bibliographic databases:

Document Type: Article

MSC: Primary 20G30; Secondary 20F05, 20C12

Language: Russian

Citation: M. A. Vsemirnov, “On (2,3)-generation of matrix groups over the ring of integers”, Algebra i Analiz, 19:6 (2007), 22–58; St. Petersburg Math. J., 19:6 (2008), 883–910

Citation in format AMSBIB

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\transl

\jour St. Petersburg Math. J.

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\vol 19

\issue 6

\pages 883--910

\crossref{https://doi.org/10.1090/S1061-0022-08-01026-1}

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Linking options:

https://www.mathnet.ru/eng/aa145

https://www.mathnet.ru/eng/aa/v19/i6/p22

Cycle of papers

On (2,3)-generation of matrix groups over the ring of integers
M. A. Vsemirnov
Algebra i Analiz, 2007, 19:6, 22–58
On $(2,3)$ -generation of matrix groups over the ring of integers, II
M. A. Vsemirnov
Algebra i Analiz, 2020, 32:5, 62–85

This publication is cited in the following 10 articles:

D. I. Shkolnik, “O $(2,3)$-porozhdenii $\mathrm{SL}_5(\mathbb{Z}_p)$”, Voprosy teorii predstavlenii algebr i grupp. 38, Zap. nauchn. sem. POMI, 513, POMI, SPb., 2022, 193–217
Ya. N. Nuzhin, “Tenzornye predstavleniya i porozhdayuschie mnozhestva involyutsii nekotorykh matrichnykh grupp”, Tr. IMM UrO RAN, 26, no. 3, 2020, 133–141
M. A. Vsemirnov, “On $(2,3)$-generation of matrix groups over the ring of integers, II”, St. Petersburg Math. J., 32:5 (2021), 865–884
Pellegrini M.A., “the (2,3)-Generation of the Special Linear Groups Over Finite Fields”, Bull. Aust. Math. Soc., 95:1 (2017), 48–53
V. L. Vasilyev, “On the $(2,3)$-generation of hyperbolic symplectic groups”, J. Math. Sci. (N. Y.), 209:4 (2015), 481–499
I. M. Pevzner, “Width of $\mathrm{GL}(6,K)$ with respect to quasi-root elements”, J. Math. Sci. (N. Y.), 209:4 (2015), 600–613
Vasilyev V.L., Vsemirnov M.A., “On the (2,3)-Generation of Hyperbolic Symplectic Groups of Large Rank”, J. Pure Appl. Algebr., 217:11 (2013), 2036–2049
Vasilyev V., Vsemirnov M., “The group $\mathrm{Sp}_{10}(\mathbb Z)$ is $(2,3)$-generated”, Cent. Eur. J. Math., 9:1 (2011), 36–49
Vasilyev V.L., Vsemirnov M.A., “On $(2,3)$-generation of low-dimensional symplectic groups over the integers”, Commun. Algebra, 38:9 (2010), 3469–3483
Tamburini M.C., “The $(2,3)$-generation of matrix groups over the integers”, Ischia group theory 2008, Sci. Publ., Hackensack, NJ, 2009, 258–264

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

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Abstract page:	551
Full-text PDF :	174
References:	75
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