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On formulae of Macbeath and Hussein

Published online by Cambridge University Press:  18 May 2009

W. W. Stothers
W. W. Stothers
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
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In his thesis [1], Hussein considered regular permutations of order 2 and 3 in Sn whose product is an n-cycle. For such a pair, we must have

for some g ≥ 1. Such a permutation pair corresponds to a free cycloidal subgroup of the classical modular group (see, e.g., [3]). Previously the free subgroups and the cycloidal subgroups of fixed genus had been enumerated ([4], [5]).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 1 , January 1989 , pp. 65 - 70
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

References

1.Omar, A. A. Hussein, On some permutation representations of (2, 3, n)-groups, Ph.D. Thesis (Birmingham, England 1979).Google Scholar
2.Macbeath, A. M., Generic Dirichlet Polygons, Glasgow Math. J. 27 (1985), 129–142.CrossRefGoogle Scholar
3.Stothers, W. W., The number of subgroups of given index in the modular group. Proc. Roy. Soc. Edinburgh 78A (1977), 105–112.CrossRefGoogle Scholar
4.Stothers, W. W., Free Subgroups of the Free Product of Cyclic Groups, Math. Comp. 32 (1978), 1274–1280.CrossRefGoogle Scholar
5.Stothers, W. W., On a result of Petersson concerning the modular group, Proc. Roy. Soc. Edinburgh 87A (1981), 263–270.CrossRefGoogle Scholar