Power subgroups of Hecke groups \(H(\sqrt n)\) (Q5945164)

Using techniques of combinatorial group theory, for each integer \(m\), the authors determine the group structure of the subgroup generated by all \(m\)th powers of elements in the Hecke group \(H(\sqrt{n})\), where \(n\geq 2\) is a square-free integer. The Hecke group \(H(\lambda)\) is the subgroup of \(\text{PSL}(2, \mathbb R)\) generated by \(z \mapsto -1/z\) and \(z \mapsto z + \lambda\).