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Docta Complutense author Bujalance García, Emilio author Etayo Gordejuela, José Javier 2023-06-21T02:02:02Z 2023-06-21T02:02:02Z 1987 Bujalance 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. 0386-5991 10.2996/kmj/1138037412 https://hdl.handle.net/20.500.14352/64651 https//doi.org/10.2996/kmj/1138037412 http://projecteuclid.org/euclid.kmj/1138037412 If 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. eng Automorphism groups of hyperelliptic Riemann surfaces journal article URL https://docta.ucm.es/bitstreams/aa701b96-357c-4cd7-a275-1f1cb05c5aaf/download File MD5 24d4251de7866e91672ecfd4fc1db965 604468 application/pdf Etayo04.pdf URL https://docta.ucm.es/bitstreams/2d57f00c-af68-4f2a-ba1a-a6ed84e18924/download File MD5 06d3f76ed3b6e9b3b55c9ca8ea5f97d7 14022 text/plain Etayo04.pdf.txt