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On the $(2,3)$-generation of hyperbolic symplectic groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 26, Tome 423 (2014), pp. 5-32 Cet article a éte moissonné depuis la source Math-Net.Ru

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For any finitely generated, commutative ring $R$ and any sufficiently large $n$, we prove that the elementary hyperbolic symplectic group $\mathrm{ESp}_{2n}(R)$ can be generated by an involution and an element of order 3. 
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V. L. Vasilyev. On the $(2,3)$-generation of hyperbolic symplectic groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 26, Tome 423 (2014), pp. 5-32. http://geodesic.mathdoc.fr/item/ZNSL_2014_423_a0/

[1] L. Di Martino, N. Vavilov, “$(2,3)$-generation of $SL(n, q)$. I. Cases $n = 5, 6, 7$”, Comm. Algebra, 22:4 (1994), 1321–1347 | DOI | MR | Zbl

[2] L. Di Martino, N. Vavilov, “$(2,3)$-generation of $SL(n, q)$. II. Cases $n\geq8$”, Comm. Algebra, 24 (1996), 487–515 | DOI | MR | Zbl

[3] A. J. Hahn, O. T. O'Meara, The classical groups and K-theory, Grundlehren Math. Wiss., 291, Springer-Verlag, Berlin, 1989 | DOI | MR | Zbl

[4] S. Lang, Introduction to Modular Forms, Springer, 1976 | MR

[5] M. W. Liebeck, A. Shalev, “Classical groups, probabilistic methods, and the $(2,3)$-generation problem”, Ann. Math. (2), 144 (1996), 77–125 | DOI | MR | Zbl

[6] A. Lucchini, M. C. Tamburini, “Classical groups of large rank as Hurwitz groups”, J. Algebra, 219:2 (1999), 531–546 | DOI | MR | Zbl

[7] P. Sanchini, M. C. Tamburini, “Constructive $(2,3)$-generation: a permutational approach”, Rend. Sem. Mat. Fis. Milano, 64 (1994), 141–158 | DOI | MR

[8] M. C. Tamburini, “Generation of certain simple groups by elements of small order”, Istit. Lombardo Accad. Sci. Lett. Rend. A, 121 (1987), 21–27 | MR

[9] M. C. Tamburini, J. S. Wilson, N. Gavioli, “On the $(2,3)$-generation on some classical groups. I”, J. Algebra, 168:1 (1994), 353–370 | DOI | MR | Zbl

[10] V. L. Vasilyev, M. A. Vsemirnov, “On $(2,3)$-generation of low-dimensional symplectic groups over the integers”, Communications Algebra, 38:9 (2010), 3469–3483 | DOI | MR | Zbl

[11] V. L. Vasilyev, M. A. Vsemirnov, “The group $\mathrm{Sp}_{10}(\mathbb Z)$ is $(2,3)$-generated”, Central European J. Math., 9:1 (2011), 36–49 | DOI | MR | Zbl

[12] V. L. Vasilyev, M. A. Vsemirnov, “On the $(2,3)$-generation of hyperbolic symplectic groups of large rank”, J. Pure Appl. Algebra, 217:11 (2013), 2036–2049 | DOI | MR | Zbl

[13] M. A. Vsemirnov, “Yavlyaetsya li gruppa $\mathrm{SL}(6,\mathbb Z)$ $(2,3)$-porozhdennoi?”, Zap. nauchn. semin. POMI, 330, 2006, 101–130 | MR | Zbl

[14] M. A. Vsemirnov, “O $(2,3)$-porozhdenii matrichnykh grupp nad koltsom tselykh chisel”, Algebra i analiz, 19:6 (2007), 22–58 | MR | Zbl

[15] M. A. Vsemirnov, “The group GL$(6, Z)$ is $(2,3)$-generated”, J. Group Theory, 10:4 (2007), 425–430 | DOI | MR | Zbl