p-Groups of automorphisms of compact non-orientable Riemann surfaces

We study p-groups of automorphisms of compact non-orientable Riemann surfaces of topological genus g≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g\ge 3$$\end{document}. We obtain upper bounds of the order of such groups in terms of p,  g and the minimal number of generators of the group. We also determine those values of g for which these bounds are sharp. Furthermore, the same kind of results are obtained when the p-group acts as the full automorphism group of the surface.