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A theorem on generation of finite orthogonal groups

Published online by Cambridge University Press:  09 April 2009

W. J. Wong
W. J. Wong
Affiliation:
University of Notre DameNotre Dame, Indiana, U.S.A.
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Presentation in terms of generators and relations for the classical finite simple groups of Lie type have been given by Steinberg and Curtis [2,4]. These presentations are useful in proving characterzation theorems for these groups, as in the author's work on the projective symplectic groups [5]. However, in some cases, the application is not quite instantaneous, and an intermediate result is needed to provide a presentation more suitable for the situation in hand. In this paper we prove such a result, for the orthogonal simple groups over finite fields of odd characteristic. In a subsequent article we shall use this to give a characterization of these groups in terms of the structure of the centralizer of an involution.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 4 , December 1973 , pp. 495 - 506
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Burnside, W., Theory of Groups of Finite Order, (New York, Dover, 1955).Google Scholar
[2]Curtis, C. W., ‘Central extensions of groups of Lie type’, Jour. für die reine u. angew. Math., 220 (1965). 174–185.Google Scholar
[3]Dickson, L. E., Linear Groups with an Exposition of the Galois Field Theory, (New York, Dover, 1958).Google Scholar
[4]Steinberg, R., Générateurs, relations et revêtements de groups algébriques, Colloque sur la Théorie des Groupes Algébriques, (Bruxelles, 1962, 113–127).Google Scholar
[5]Wong, W. J., ‘Characterization of the finite simple groups PSp2n(q)’, Jour. of Algebra 14 (1970), 531–551.CrossRefGoogle Scholar