Etayo Gordejuela, José JavierMartínez García, Ernesto2023-06-202023-06-202005Etayo Gordejuela, J. J., & Martínez García, E. «Alternating Groups, Hurwitz Groups and H * -Groups». Journal of Algebra, vol. 283, n.o 1, enero de 2005, pp. 327-49. DOI.org (Crossref), https://doi.org/10.1016/j.jalgebra.2004.07.039.0021-869310.1016/j.jalgebra.2004.07.039https://hdl.handle.net/20.500.14352/50029The authors obtain the pairs of generators, necessary to study the non-orientable case, of the alternating groups $A_n$ for $n=15$, 21, 22, 28 and 29, which are also Hurwitz groups, groups with maximal number of automorphisms on Riemann surfaces. The results found here can be applied to handle the corresponding problem on non-orientable surfaces. In particular, they show that the ones for $n=15$ and 28 match the bound for non-orientable surfaces, while the ones for $n=21$, 22 and 29 do not. They also obtain some other Hurwitz groups which are at the same time proper subgroups of the alternating groups. They obtain a way of deciding which alternating groups are also $H^*$-groups.engjournal articlehttps//doi.org/10.1016/j.jalgebra.2004.07.039http://www.sciencedirect.com/science/article/pii/S0021869304004259restricted access521.7AutomorphismsRiemann surfacesWeierstrass pointsGap sequencesGeometria algebraica1201.01 Geometría Algebraica