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A Presentation of the Groups PSL(2, p)

Published online by Cambridge University Press:  20 November 2018

H. Behr  and
J. Mennicke
H. Behr
Affiliation:
Maihematisches Institut der Universität, Göttingen
J. Mennicke
Affiliation:
Maihematisches Institut der Universität, Göttingen
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In the present paper, we shall prove the following result.

Theorem A. The groups PSL(2, p) can be presented by the following system of generators and relations:

1.1

This theorem considerably improves earlier results of Bussey, Frasch, and Todd (cf. 2, pp. 93-96). The presentation of Frasch reads as follows:

1.2

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1432 - 1438
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Behr, H., Über die endliche Definierbarkeit verallgemeinerter Einheitengruppen, J. Reine Angew. Math. 211 (1962), 123–135.Google Scholar
2. Coxeter, H. S. M. and Moser, W. O. J., Generators and relations for discrete groups (Springer-Verlag, Berlin, 1957).10.1007/978-3-662-25739-5CrossRefGoogle Scholar
3. Mennicke, J., On Ihara's modular groups. I (mimeographed notes, University of Gôttingen, April, 1967).Google Scholar
4. Mennicke, J., On Ihara's modular group, Invent. Math. 4 (1967), 202–228.Google Scholar