### Impacto

Etayo Gordejuela, J. Javier and Martínez García, Ernesto
(2006)
*Alternating groups as automorphism groups of Riemann surfaces.*
International Journal of Algebra and Computation, 16
(1).
pp. 91-98.
ISSN 0218-1967

Official URL: http://www.worldscinet.com/ijac/16/1601/S0218196706002937.html

## 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.

Item Type: | Article |
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Uncontrolled Keywords: | Automorphisms; Fuchsian groups and their generalizations; Compact Riemann surfaces and uniformization; Klein surfaces |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 15792 |

References: | N. L. Alling and N. Greenleaf, Foundations of the Theory of Klein Surfaces, Lecture Notes in Mathematics, Vol. 219 (Springer, Berlin-Heidelberg-New York, 1971). M. D. E. Conder, Some results on quotients of triangle groups, Bull. Austral. Math. Soc. 29 (1984) 73–90. J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, The ATLAS of Finite Groups (Oxford University Press, 1985). J. J. Etayo and E. Martínez, Alternating groups, Hurwitz groups and H ∗ -groups, J. Algebra 283 (2005) 327–349. A. M. Macbeath, The classification of non-Euclidean crystallographic groups, Canad. J. Math. 6 (1967) 1192–1205. C. L. May, Large automorphism groups of compact Klein surfaces with boundary, Glasgow Math. J. 18 (1977) 1–10. R. Preston, Projective structures and fundamental domains on compact Klein surfaces, Thesis, University of Texas (1975). D. Singerman, Automorphisms of compact non-orientable Riemann surfaces, Glasgow Math. J. 12 (1971) 50–59. D. Singerman, On the structure of non-Euclidean crystallographic groups, Proc. Cambridge Phil. Soc. 76 (1974) 233–240. H. C. Wilkie, On non-Euclidean crystallographic groups, Math. Z. 91 (1966) 87–102. |

Deposited On: | 28 Jun 2012 09:30 |

Last Modified: | 28 Jun 2012 09:30 |

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