Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T14:09:47.757Z Has data issue: false hasContentIssue false
  • English
  • Français

On (2, 3, 7)-generation of maximal parabolic subgroups

Part of: Special aspects of infinite or finite groups Other groups of matrices

Published online by Cambridge University Press:  09 April 2009

L. Di Martino  and
M. C. Tamburini
L. Di Martino
Affiliation:
Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Via Bicocca degli Arcimboldi 8, Ed. U7 20126 Milano, Italy e-mail: [email protected]
M. C. Tamburini
Affiliation:
Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via Musei 41, 25121 Brescia, Italy e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let R be a ring with 1 and En (R) be the subgroup of GLn(R) generated by the matrices I + reij, r ∈ R, i ≠ j. We prove that the subgroup of consisting of the matrices of shape , where and , is (2, 3, 7)-generated whenever R is finitely generated and n, are large enough.

Keywords

Hurwitz groupsparabolic subgroups

MSC classification

Secondary: 20F05: Generators, relations, and presentations 20H25: Other matrix groups over rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 2 , October 2001 , pp. 187 - 200
Copyright
Copyright © Australian Mathematical Society 2001

References

[Co]Conder, M., ‘Generators for alternating and symmetric groups’, J. London Math. Soc. (2) 22 (1980), 75–86.CrossRefGoogle Scholar
[HO'M]Hahn, A. J. and O'Meara, O. T., The classical groups and K -theory (Springer, Berlin, 1989).CrossRefGoogle Scholar
[LT]Lucchini, A. and Tamburini, M. C., ‘Classical groups of large rank as Hurwitz groups’, J. Algebra 219 (1999), 531–546.CrossRefGoogle Scholar
[LTW]Lucchini, A., Tamburini, M. C. and Wilson, J. S., ‘Hurwitz groups of large rank’, J. London Math. Soc. (2) 61 (2000), 81–92.CrossRefGoogle Scholar
[Mo]Molinari, D., Le 17 rappresentazioni di Conder del gruppo Δ(2, 3, 7) (Tesi di laurea, Università Cattolica del Sacro Cuore, Brescia, 1998).Google Scholar