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On Hurwitz extensions by PSL2(7)

Published online by Cambridge University Press:  24 October 2008

Jeffrey M. Cohen
Jeffrey M. Cohen
Affiliation:
University of Pittsburgh
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Abstract

In this paper, a new family of factors of (2, 3, 7) is obtained which contains groups found in three other papers. It is shown that for all n, there exists an m such that there are at least n isomorphism types of Hurwitz groups of order m. Finally, presentations for all groups considered are obtained.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 3 , November 1979 , pp. 395 - 400
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

REFERENCES

(1)Cohen, J. M. Some compact Riemann surfaces via Fuchsian groups. (Submitted.)Google Scholar
(2)Hurwitz, A.Über algebraische Gebilde mit eindeutigen Transformationen in sich. Math. Annalen 41 (1893), 403–442.CrossRefGoogle Scholar
(3)Klein, F.Über die Transformationen siebenter Ordnung der elliptischen Funktionen. Math. Annalen 14 (1879), 428–471.CrossRefGoogle Scholar
(4)Leech, J.Generators for certain normal subgroups of (2, 3, 7). Proc. Cambridge Philos. Soc. 61 (1965), 321–332.CrossRefGoogle Scholar
(5)Leech, J.Note on the abstract group (2, 3, 7; 9). Proc. Cambridge Philos. Soc. 62 (1966), 7–10.CrossRefGoogle Scholar
(6)Macbeath, A. M.On a theorem of Hurwitz. Proc. Glasgow Math. Assoc. 5 (1961), 90–96.CrossRefGoogle Scholar
(7)Macbeath, A. M.On a curve of genus 7. Proc. London Math. Soc. (3) 15 (1965), 527–542.CrossRefGoogle Scholar
(8)Mumford, D.Curves and Their Jacobians (The University of Michigan Press, Ann Arbor, 1975).Google Scholar
(9)Sinkov, A.On the group-defining relations (2, 3, 7: P), Ann. Math. 38 (1937), 577–584.CrossRefGoogle Scholar
(10)Sinkov, A.Necessary and sufficient conditions for generating certain simple groups by two operators of periods two and three. Amer. J. Math. 50 (1937), 67–76.CrossRefGoogle Scholar