In this work a new proof of the fact that the group structure of the Hecke groups is isomorphic to the free product of two cyclic groups of orders 2 and q is given The method used in the proof requires a result of A.M. Macbeath together with the notion of fundamental region. Also given are some new results on the parabolic points of Hecke groups, which still is an open problem.
CANGÜL, İ. N. (1996) "THE GROUP STRUCTURE OF HECKE GROUPS H(\lambda_q)," Turkish Journal of Mathematics: Vol. 20: No. 2, Article 9. Available at: https://journals.tubitak.gov.tr/math/vol20/iss2/9