On extendability of group actions on compact Riemann surfaces

Authors:
Emilio Bujalance, F. J. Cirre and Marston Conder

Journal:
Trans. Amer. Math. Soc. **355** (2003), 1537-1557

MSC (2000):
Primary 20H10; Secondary 14H55, 20F38, 30F10

DOI:
https://doi.org/10.1090/S0002-9947-02-03184-7

Published electronically:
December 4, 2002

MathSciNet review:
1946404

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Abstract | References | Similar Articles | Additional Information

Abstract: The question of whether a given group which acts faithfully on a compact Riemann surface of genus is the full group of automorphisms of (or some other such surface of the same genus) is considered. Conditions are derived for the extendability of the action of the group in terms of a concrete partial presentation for associated with the relevant branching data, using Singerman's list of signatures of Fuchsian groups that are not finitely maximal. By way of illustration, the results are applied to the special case where is a non-cyclic abelian group.

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Additional Information

**Emilio Bujalance**

Affiliation:
Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, c/ Senda del Rey s/n, 28040 Madrid, Spain

Email:
eb@mat.uned.es

**F. J. Cirre**

Affiliation:
Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, c/ Senda del Rey s/n, 28040 Madrid, Spain

Email:
jcirre@mat.uned.es

**Marston Conder**

Affiliation:
Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand

Email:
conder@math.auckland.ac.nz

DOI:
https://doi.org/10.1090/S0002-9947-02-03184-7

Keywords:
Riemann surface,
automorphism group

Received by editor(s):
December 10, 2001

Published electronically:
December 4, 2002

Additional Notes:
The first author was partially supported by DGICYT PB98-0017

The second author was partially supported by DGICYT PB98-0756

The third author was partially supported by N.Z. Marsden Fund UOA-810

Article copyright:
© Copyright 2002
American Mathematical Society