## On extendability of group actions on compact Riemann surfaces

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- by Emilio Bujalance, F. J. Cirre and Marston Conder PDF
- Trans. Amer. Math. Soc.
**355**(2003), 1537-1557 Request permission

## Abstract:

The question of whether a given group $G$ which acts faithfully on a compact Riemann surface $X$ of genus $g\ge 2$ is the full group of automorphisms of $X$ (or some other such surface of the same genus) is considered. Conditions are derived for the extendability of the action of the group $G$ in terms of a concrete partial presentation for $G$ 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 $G$ is a non-cyclic abelian group.## References

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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
- MR Author ID: 43085
- 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
- MR Author ID: 601436
- Email: jcirre@mat.uned.es
**Marston Conder**- Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
- MR Author ID: 50940
- ORCID: 0000-0002-0256-6978
- Email: conder@math.auckland.ac.nz
- 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 - © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1946404