Etayo Gordejuela, José Javier2023-06-212023-06-211985Etayo Gordejuela, J. J. «Non-Orientable Automorphisms of Riemann Surfaces». Archiv Der Mathematik, vol. 45, n.o 4, octubre de 1985, pp. 374-84. DOI.org (Crossref), https://doi.org/10.1007/BF01198242.0003-889X10.1007/BF01198242https://hdl.handle.net/20.500.14352/64647We study cyclic groups of automorphisms of Riemann surfaces that contain non-orientable elements. We obtain conditions for such a group, and calculate the minimum possible genus of the surface on which it acts. As a consequence of these results we obtain that the order of a sense- reversing automorphism of a Riemann surface of genus g is at most $4g+4$ for even g and 4g-4 for odd g, and that both bounds are attained for every g.journal articlehttps//doi.org/10.1007/BF01198242http://www.springerlink.com/content/t947r671t51r1152/references/metadata only access512.54Fuchsian groups and automorphic functionsFinite automorphism groups of miscellaneous structuresCyclic groups of automorphisms of Riemann surfacesNon-orientable elementsGenusSense-reversing automorphismGrupos (Matemáticas)