Bujalance García, EmilioGamboa Mutuberria, José ManuelMartens, GerrietEtayo Gordejuela, José Javier2023-06-202023-06-201989Bujalance García, E., Gamboa Mutuberria, J. M., Martens, G. & Etayo Gordejuela, J. J. «Minimal Genus of Klein Surfaces Admitting an Automorphism of a given Order». Archiv Der Mathematik, vol. 52, n.o 2, febrero de 1989, pp. 191-202. DOI.org (Crossref), https://doi.org/10.1007/BF01191274.0003-889X10.1007/BF01191274https://hdl.handle.net/20.500.14352/57398Let K be a compact Klein surface of algebraic genus $g\ge 2,$ which is not a classical Riemann surface. The authors show that if K admits an automorphism of order $N>2,$ then it must have algebraic genus at least $(p\sb 1-1)N/p\sb 1$ if N is prime or if its smallest prime factor, $p\sb 1$, occurs with exponent 1 in N. Otherwise the genus is at least $(p\sb 1-1)(N/p\sb 1-1)$. This result extends to bordered Klein surfaces a result of {\it E. Bujalance} [Pac. J. Math. 109, 279-289 (1983)] and is the analog for Klein surfaces of a result of {\it W. J. Harvey} [Q. J. Math., Oxf. II. Ser. 17, 86-97 (1966)] and, ultimately, of {\it A. Wiman} [Kongl. Svenska Vetenskaps-Akad. Handl., Stockholm 21, No.1 and No.3 (1895)].journal articlehttps//doi.org/10.1007/BF01191274http://www.springerlink.com/content/p60j7tu265313n66/metadata only access512.7Classification theory of Riemann surfacesReal ground fieldsCurvesFuchsian groups and their generalizationsGeometria algebraica1201.01 Geometría Algebraica