On formulae of Macbeath and Hussein
Wilson Stothers · Glasgow Mathematical Journal · 1989
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]).