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Minimal genus of Klein surfaces admitting an automorphism of a given order Bujalance García, Emilio Gamboa Mutuberria, José Manuel Martens, Gerriet Etayo Gordejuela, José Javier 512.7 Classification theory of Riemann surfaces Real ground fields Curves Fuchsian groups and their generalizations Geometria algebraica 1201.01 Geometría Algebraica Let 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)]. Comisión Asesora de Investigación Cientifica y Técnica Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T16:54:36Z 2023-06-20T16:54:36Z 1989 journal article https://hdl.handle.net/20.500.14352/57398 0003-889X 10.1007/BF01191274 Bujalance 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. metadata only access Birkhäuser Verlag