  Conformal/anticonformal actions of the quasi-abelian group $QA_{n}$ of order
$2^n$, for $n\geq 4$, on closed Riemann surfaces, pseudo-real Riemann surfaces
and closed Klein surfaces are considered. We obtain several consequences, such
as the solution of the minimum genus problem for the $QA_n$-actions, and for
each of these actions, we study the topological rigidity action problem. In the
case of pseudo-real surfaces, attention was typically restricted to group
actions that admit anticonformal elements. In this paper we consider two cases:
either $QA_n$ has anticonformal elements or only contains conformal elements.

Algebraic Geometry