Bujalance García, EmilioEtayo Gordejuela, José Javier2023-06-202023-06-2019880002-9939https://hdl.handle.net/20.500.14352/57394A bordered Klein surface of algebraic genus p has at most 12(p-1) automorphisms and this is attained for infinitely many values of p. Furthermore, for an infinity of values of p, the largest group of automorphisms of such a surface is $4(p+1)$ or 4p depending on whether the surface is orientable or not [{\it C. L. May}, Pac. J. Math. 59, 199- 210 (1975) and Proc. Am. Math. Soc. 63, 273-280 (1977]. \par Here the authors examine such surfaces which are additionally hyperelliptic and have automorphism groups of order exceeding 4(p-1). Using their characterization of hyperelliptic Klein surface via non- Euclidean crystallographic groups [Q. J. Math., Oxf. II. Ser. 36, 141-157 (1985)] the authors determine these automorphism groups, which are all dihedral or direct sums of a dihedral group and a cyclic group of order 2, and the corresponding topological type of the surface.engjournal articlehttp://www.jstor.org/stable/2046834http://www.jstor.org/restricted access512.7Fuchsian groups and their generalizationsCurvesCompact Riemann surfaces and uniformizationGeometria algebraica1201.01 Geometría Algebraica