Extensions of finite cyclic group actions on non-orientable surfaces
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- by E. Bujalance, F.J. Cirre and M.D.E. Conder PDF
- Trans. Amer. Math. Soc. 365 (2013), 4209-4227 Request permission
Abstract:
Conditions are derived for the extension of an action of a cyclic group on a compact non-orientable surface to the faithful action of some larger group on the same surface. It is shown that if such a cyclic action is realised by means of a non-maximal NEC signature, then the action always extends. The special case where the full automorphism group is cyclic of the largest possible order (for given genus) is also considered. This extends previous work by the authors for group actions on orientable surfaces. In addition, the smallest algebraic genus of a non-orientable surface on which a given cyclic group acts as the full automorphism group is determined.References
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Additional Information
- E. 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
- M.D.E. Conder
- Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
- MR Author ID: 50940
- ORCID: 0000-0002-0256-6978
- Email: m.conder@auckland.ac.nz
- Received by editor(s): May 17, 2011
- Received by editor(s) in revised form: November 19, 2011
- Published electronically: February 18, 2013
- Additional Notes: The first author was partially supported by MTM2011-23092
The second author was partially supported by MTM2011-23092
The third author was partially supported by the N.Z. Marsden Fund UOA-1015 - © Copyright 2013 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 365 (2013), 4209-4227
- MSC (2010): Primary 57M60; Secondary 14H37, 20H15, 30F50
- DOI: https://doi.org/10.1090/S0002-9947-2013-05776-5
- MathSciNet review: 3055694