### Impacto

Etayo Gordejuela, J. Javier
(1985)
*On the order of automorphism groups of Klein surfaces.*
Glasgow Mathematical Journal, 26
.
pp. 75-81.
ISSN 0017-0895

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Official URL: http://journals.cambridge.org/abstract_S0017089500005796

## Abstract

A problem of special interest in the study of automorphism groups of surfaces are the bounds of the orders of the groups as a function of the genus of the surface. May has proved that a Klein surface with boundary of algebraic genus p has at most 12(p–1) automorphisms. In this paper we study the highest possible prime order for a group of automorphisms of a Klein surface. This problem was solved for Riemann surfaces by Moore in. We shall use his results for studying the Klein surfaces that are not Riemann surfaces. The more general result that we obtain is the following: if X is a Klein surface of algebraic genus p, and G is a group of automorphisms of X, of prime order n, then n ≤ p + 1.

Item Type: | Article |
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Uncontrolled Keywords: | non-Euclidean crystallographic group; Klein surface; group of automorphisms |

Subjects: | Sciences > Mathematics > Group Theory |

ID Code: | 15746 |

References: | N. L. Ailing, Real elliptic curves. Notes of Math. 54, (North-Holland, 1981). N. L. Ailing and N. Greenleaf, Foundations of the theory of Klein surfaces. Lecture Notes in Math. 219, (Springer-Verlag, 1971). E. Bujalance, Normal subgroups of NEC groups, Math. Z. 178 (1981) 331-341. E. Bujalance, Cyclic groups of automorphisms of compact non-orientable Klein surfaces without boundary, Pacific J. of Math. 109 (1983) 279-289. E. Bujalance, Automorphisms groups of compact Klein surfaces with one boundary component, (to appear). E. Bujalance and J. M. Gamboa, Automorphisms groups of algebraic curves of R" of genus 2, Archiv der Math. 42 (1984) 229-237. J. J. Etayo, NEC subgroups in Klein surfaces. Bol. Soc. Mat. Mex. (to appear). C. L. May, Large automorphism groups of compact Klein surfaces with boundary, Glasgow Math. J. 18 (1977) 1-10. C. L. May, A bound for the number of automorphisms of a compact Klein surface with boundary, Proc. Amer. Math. Soc. 63 (1977) 273-280. M. J. Moore, Fixed points of automorphisms of compact Riemann surfaces, Can. J. Math. 22 (1970) 922-932. S. M. Natanzon, Automorphisms of the Riemann surface of an M-curve, Fund Anal, and Appl. 12 (1978) 228-229. R. Preston, Projective structures and fundamental domains on compact Klein surfaces, (Ph.D. thesis. Univ. of Texas, 1975). D. Singerman, On the structure of non-euclidean crystallographic groups, Proc. Cambridge Phil. Soc. 76 (1974) 233-240. |

Deposited On: | 25 Jun 2012 08:34 |

Last Modified: | 06 Feb 2014 10:30 |

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