The group Sp10(ℤ) is (2,3)-generated

Vadim Vasilyev; Maxim Vsemirnov

Open Mathematics (2011)

  • Volume: 9, Issue: 1, page 36-49
  • ISSN: 2391-5455

Abstract

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It is proved that the group Sp10(ℤ) is generated by an involution and an element of order 3.

How to cite

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Vadim Vasilyev, and Maxim Vsemirnov. "The group Sp10(ℤ) is (2,3)-generated." Open Mathematics 9.1 (2011): 36-49. <http://eudml.org/doc/269596>.

@article{VadimVasilyev2011,
abstract = {It is proved that the group Sp10(ℤ) is generated by an involution and an element of order 3.},
author = {Vadim Vasilyev, Maxim Vsemirnov},
journal = {Open Mathematics},
keywords = {Symplectic groups; (2; 3)-generation; Symplectic transvections; symplectic groups; -generations; symplectic transvections},
language = {eng},
number = {1},
pages = {36-49},
title = {The group Sp10(ℤ) is (2,3)-generated},
url = {http://eudml.org/doc/269596},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Vadim Vasilyev
AU - Maxim Vsemirnov
TI - The group Sp10(ℤ) is (2,3)-generated
JO - Open Mathematics
PY - 2011
VL - 9
IS - 1
SP - 36
EP - 49
AB - It is proved that the group Sp10(ℤ) is generated by an involution and an element of order 3.
LA - eng
KW - Symplectic groups; (2; 3)-generation; Symplectic transvections; symplectic groups; -generations; symplectic transvections
UR - http://eudml.org/doc/269596
ER -

References

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  1. [1] Di Martino L., Vavilov N., (2; 3)-generation of SL(n, q). I. Cases n = 5, 6, 7, Comm. Algebra, 1994, 22(4), 1321–1347 http://dx.doi.org/10.1080/00927879408824908 Zbl0805.20038
  2. [2] Di Martino L., Vavilov N., (2; 3)-generation of SL(n, q). II. Cases n ≥ 8, Comm. Algebra, 1996, 24(2), 487–515 http://dx.doi.org/10.1080/00927879608825582 Zbl0847.20043
  3. [3] Hahn A.J., O'Meara O.T., The Classical Groups and K-theory, Grundlehren Math. Wiss., 291, Springer, Berlin, 1989 
  4. [4] Liebeck M.W., Shalev A., Classical groups, probabilistic methods, and the (2, 3)-generation problem, Ann. of Math., 1996, 144(1), 77–125 http://dx.doi.org/10.2307/2118584 Zbl0865.20020
  5. [5] Lucchini A., Tamburini M.C., Classical groups of large rank as Hurwitz groups, J. Algebra, 1999, 219(2), 531–546 http://dx.doi.org/10.1006/jabr.1999.7911 Zbl1063.20504
  6. [6] Sanchini P., Tamburini M.C., Constructive (2; 3)-generation: a permutational approach, Rend. Sem. Mat. Fis. Milano, 1994, 64(1), 141–158 http://dx.doi.org/10.1007/BF02925196 Zbl0860.20039
  7. [7] Tamburini M.C., The (2; 3)-generation of matrix groups over the integers, In: Ischia Group Theory 2008, Proceedings of the Conference in Group Theory, Naples, April 1–4, 2008, World Scientific, Hackensack, 2009, 258–264 http://dx.doi.org/10.1142/9789814277808_0020 
  8. [8] Tamburini M.C., Generation of certain simple groups by elements of small order, Istit. Lombardo Accad. Sci. Lett. Rend. A, 1987, 121, 21–27 
  9. [9] Tamburini M.C., Wilson J.S., Gavioli N., On the (2, 3)-generation on some classical groups. I, J. Algebra, 1994, 168(1), 353–370 http://dx.doi.org/10.1006/jabr.1994.1234 
  10. [10] Vasilyev V.L., Vsemirnov M.A., On (2, 3)-generation of low-dimensional symplectic groups over the integers, Comm. Algebra, 2010, 38(9), 3469–3483 http://dx.doi.org/10.1080/00927870902933205 Zbl1208.20036
  11. [11] Vsemirnov M.A., Is the group SL(6,ℤ) (2, 3)-generated?, J. Math. Sci. (N.Y.), 2007, 140(5), 660–675 http://dx.doi.org/10.1007/s10958-007-0006-8 
  12. [12] Vsemirnov M.A., The group GL(6,ℤ) is (2, 3)-generated, J. Group Theory, 2007, 10(4), 425–430 http://dx.doi.org/10.1515/JGT.2007.033 
  13. [13] Vsemirnov M.A., On (2, 3)-generation of matrix groups over the ring of integers, St. Petersburg Math. J., 2008, 19(6), 883–910 http://dx.doi.org/10.1090/S1061-0022-08-01026-1 Zbl1206.20040
  14. [14] Vsemirnov M.A., On (2, 3)-generation of matrix groups over the ring of integers. II, St. Petersburg Math. J. (in press) 

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