Geodesic
On formulae of Macbeath and Hussein
Glasgow mathematical journal, Tome 31 (1989) no. 1, pp. 65-70

Voir la notice de l'article provenant de la source Cambridge University Press

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 havefor 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]). 
Stothers, W. W. On formulae of Macbeath and Hussein. Glasgow mathematical journal, Tome 31 (1989) no. 1, pp. 65-70. doi: 10.1017/S0017089500007552
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[1] 1.Omar, A. A. Hussein, On some permutation representations of (2, 3, n)-groups, Ph.D. Thesis (Birmingham, England 1979). Google Scholar

[2] 2.Macbeath, A. M., Generic Dirichlet Polygons, Glasgow Math. J. 27 (1985), 129–142. Google Scholar | DOI

[3] 3.Stothers, W. W., The number of subgroups of given index in the modular group. Proc. Roy. Soc. Edinburgh 78A (1977), 105–112. Google Scholar | DOI

[4] 4.Stothers, W. W., Free Subgroups of the Free Product of Cyclic Groups, Math. Comp. 32 (1978), 1274–1280. Google Scholar | DOI

[5] 5.Stothers, W. W., On a result of Petersson concerning the modular group, Proc. Roy. Soc. Edinburgh 87A (1981), 263–270. Google Scholar | DOI

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