Bujalance García, EmilioEtayo Gordejuela, José Javier2023-06-212023-06-211987Bujalance García, E. & Etayo Gordejuela, J. J. «Automorphism groups of hyperelliptic Riemann surfaces». Kodai Mathematical Journal, vol. 10, n.o 2, enero de 1987. DOI.org (Crossref), https://doi.org/10.2996/kmj/1138037412.0386-599110.2996/kmj/1138037412https://hdl.handle.net/20.500.14352/64651If G is a group of automorphisms of a hyperelliptic Riemann surface of genus g represented as D/$\Gamma$ where D is the hyperbolic plane and $\Gamma$ a Fuchsian group, then $G\cong \Gamma '/\Gamma$ where $\Gamma$ ' is also a Fuchsian group. Furthermore G contains a central subgroup $G\sb 1$ of order 2 and if $\Gamma\sb 1$ is the corresponding subgroup of $\Gamma$ ', then $G/G\sb 1$ is a group of automorphisms of the sphere $D/\Gamma\sb 1$. Using this and structure theorem for Fuchsian groups the authors determine all surfaces of genus $g>3$ admitting groups G with $o(G)>8(g-1)$. There are two infinite families both corresponding to $\Gamma$ ' being the triangle group (2,4,m) and six other groups.engjournal articlehttps//doi.org/10.2996/kmj/1138037412http://projecteuclid.org/euclid.kmj/1138037412restricted access512.7Classification theory of Riemann surfacesCoveringsFundamental groupSpecial curves and curves of low genusGeometria algebraica1201.01 Geometría Algebraica