ON CONJUGACY OF p-GONAL AUTOMORPHISMS

Title & Authors
ON CONJUGACY OF p-GONAL AUTOMORPHISMS
Hidalgo, Ruben A.;

Abstract
In 1995 it was proved by Gonz$\small{\acute{a}}$lez-Diez that the cyclic group generated by a p-gonal automorphism of a closed Riemann surface of genus at least two is unique up to conjugation in the full group of conformal automorphisms. Later, in 2008, Gromadzki provided a different and shorter proof of the same fact using the Castelnuovo-Severi theorem. In this paper we provide another proof which is shorter and is just a simple use of Sylow`s theorem together with the Castelnuovo-Severi theorem. This method permits to obtain that the cyclic group generated by a conformal automorphism of order p of a handlebody with a Kleinian structure and quotient the three-ball is unique up to conjugation in the full group of conformal automorphisms.
Keywords
Riemann surfaces;conformal automorphisms;fixed points;
Language
English
Cited by
1.
On automorphisms groups of cyclic p-gonal Riemann surfaces, Journal of Symbolic Computation, 2013, 57, 61
2.
On the uniqueness of (p, h)-gonal automorphisms of Riemann surfaces, Archiv der Mathematik, 2012, 98, 6, 591
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