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Resumen:
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The authors obtain the pairs of generators, necessary to study the non-orientable case, of the alternating groups $A_n$ for 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 and 28 match the bound for non-orientable surfaces, while the ones for 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.
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