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On the order of automorphism groups of Klein surfaces

Published online by Cambridge University Press:  18 May 2009

J. J. Etayo Gordejuela
J. J. Etayo Gordejuela
Affiliation:
Departamento de Geometría y Topología, Facultad de Ciencias Matemáticas, Universidad Complutense, Madrid, Spain
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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 [9].

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 [10]. 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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 26 , Issue 1 , January 1985 , pp. 75 - 81
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

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