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Presentations of the Groups SL(2, m) And PSL(2, m)

Published online by Cambridge University Press:  20 November 2018

J. G. Sunday
J. G. Sunday*
Affiliation:
University of Toronto, Toronto, Ontario
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In this paper, we refine the presentations of Behr and Mennicke [1] for SL(2, m) and PSL(2, m) where m is odd. The group SL(2, m) is first shown to be presented by the following system of generators and relations:

1.1

The group PSL(2, m) appears as the factor group

1.2

This simplification then permits us to use the results of Schur [3] to establish three-relation presentations for these groups.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 1129 - 1131
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Behr, H. and Mennicke, J., A Presentation of the groups PSL(2, p), Can. J. Math. 20 (1968), 1432–1438.Google Scholar
2. Gunning, R. C., Lectures on modular forms (Princeton University Press, Princeton, 1962).Google Scholar
3. Schur, J., Untersuchungen uber die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen, J. Reine Angew. Math. 132 (1907), 85–137.Google Scholar
4. Zassenhaus, H. J., A Presentation of the groups PSL(2, p) with three defining relations, Can. J. Math. 21 (1969), 310–311.Google Scholar