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On the problem of finding the full automorphism group of a compact Klein surface

Cirre, F.J. and Gamboa Mutuberria, José Manuel (2000) On the problem of finding the full automorphism group of a compact Klein surface. In Contribuciones Matemáticas. Homenaje al Prof. D. Joaquín Arregui Fernández. Universidad Complutense de Madrid, pp. 105-126. ISBN 84-7491-581-3

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Abstract

The paper under review surveys most known results about the following problem: let $X$ be a compact topological surface of algebraic genus $p>1$, with or without boundary, orientable or not. How to calculate all groups acting as the full automorphism group of some structure of Klein surface having $X$ as underlying topological surface? It must be remarked that from Riemann's uniformization theorem, and since $\Aut(X)$ has no more than 168 $(p-1)$ automorphisms (including the orientation-reversing ones), this problem is of a finite nature. In practice this is an unaccessible task except for low values of $p$ or some extra conditions on the surfaces one is dealing with.

Item Type:Book Section
Uncontrolled Keywords:automorphism groups; n.e.c. group; algebraic equation; Klein surfaces
Subjects:Sciences > Mathematics > Algebra
ID Code:17249
Deposited On:28 Nov 2012 10:13
Last Modified:28 Nov 2012 10:13

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