| Let \(QA_n\) be the quasi-abelian group of order \(2^n\). In this talk, we describe the triangular conformal actions of the group \(QA_n\) on closed Riemann surfaces of genus \(g\geq 2\). As a consequence of these triangular actions we obtain that, up to isomorphisms, there is exactly two regular dessin d'enfant with automorphism group \(QA_n\). Finally, we observe that the minimal genus over which \(QA_n\) acts purely-non-free is \(\sigma_p(QA_n)=2^{n-2}-1\) (this coincides with the strong symmetric genus of \(QA_n\)) and, up homeomorphisms, this minimal conformal action of \(QA_n\) is unique. This is part of my Ph.D. Thesis, under the adviser Saúl Quispe and Rubén A. Hidalgo. |
