Etayo Gordejuela, José JavierMartínez García, ErnestoIzquierdo, MilagrosBroughton, S. AllenCosta, Antonio F.Rodríguez, Rubí E.2023-06-192023-06-192014Etayo Gordejuela, J. J. & Martínez García, E. Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces. American Mathematical Society, 2014. DOI.org (Crossref), https://doi.org/10.1090/conm/629.978-1-4704-1093-310.1090/conm/629https://hdl.handle.net/20.500.14352/35791Proceedings of the conference on Riemann and Klein Surfaces, Symmetries and Moduli Spaces, in honor of Emilio Bujalance, held from June 24–28, 2013, at Linköping University, SwedenThe minimum genus problem consists on determining the minimum algebraic genus of a surface on which a given group G acts. For cyclic groups G this problem on bordered Klein surfaces was solved in 1989. The next step is to fix the number of boundary components of the surface and to obtain the minimum algebraic genus, and so the minimum topological genus. It was achieved for cyclic groups of prime and prime-power order in the nineties. In this work the corresponding results for cyclic groups of order N = 2q, where q is an odd prime, are obtained. There appear different results depending on the orientability of the surface. Finally, using the above mentioned results and those of this paper, we state explicitly, the general values for arbitrary number of boundary components, which are valid for each N < 12, and show how to deal with N = 12.book parthttps//doi.org/10.1090/conm/629http://www.ams.org/books/conm/629/metadata only access517.545512.541.5Klein surfacesAlgebraic genusBoundary componentsFunciones (Matemáticas)Grupos (Matemáticas)1202 Análisis y Análisis Funcional