On Thompson's finiteness theorem. (Q1770452)

The author gives an alternative (constructive) proof of Thompson's finiteness theorem for a family of congruence subgroups of the modular group. If \(G\) is a subgroup of \(\text{PSL}(2,\mathbb{R})\) commensurable with the modular group, then Thompson's theorem says that its Euler characteristic is given in terms of the orders of non-conjugate classes of elliptic elements, its genus and the parabolic class number.