Normal forms of generating pairs for Fuchsian and related groups
It is worth and very helpful to understand the set of all generating pairs of a two-generator group \(G\) via Nielsen equivalence classes and the action of \(\text{GL}(2,\mathbb{Z})\) on the set of conjugacy classes of generating pairs. Here this is done for \(G\) a non-triangular Fuchsian group or a group of the type \(\langle a,b\mid a^p=b^q\rangle\).
scientific article; zbMATH DE number 1747305