Alternating groups as automorphism groups of Riemann surfaces
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2006
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World Scientific
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Etayo Gordejuela, J. J., & Martínez García, E. «ALTERNATING GROUPS AS AUTOMORPHISM GROUPS OF RIEMANN SURFACES». International Journal of Algebra and Computation, vol. 16, n.o 01, febrero de 2006, pp. 91-98. DOI.org (Crossref), https://doi.org/10.1142/S0218196706002937.
Abstract
In this work we give pairs of generators (x, y) for the alternating groups An, 5 ≤ n ≤ 19, such that they determine the minimal genus of a Riemann surface on which An acts as the automorphism group. Using these results we prove that A15 is the unique of these groups that is an H*-group, i.e., the groups achieving the upper bound of the order of an automorphism group acting on non-orientable unbordered surfaces.