%0 Journal Article
%A Bujalance García, Emilio
%A Gamboa Mutuberria, José Manuel
%A Martens, Gerriet
%A Etayo Gordejuela, José Javier
%T Minimal genus of Klein surfaces admitting an automorphism of a given order
%D 1989
%@ 0003-889X
%U https://hdl.handle.net/20.500.14352/57398
%X 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)].
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