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On formulae of Macbeath and Hussein
Published online by Cambridge University Press: 18 May 2009
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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]).
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- 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
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