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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]
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Abstract

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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

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