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Journal of the London Mathematical Society 1999 59(2):573-584; doi:10.1112/S0024610799007115
© 1999 by London Mathematical Society
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© The London Mathematical Society

On Cyclic Groups of Automorphisms of Riemann Surfaces

Emilio Bujalance and Marston Conder

Departamento de Matemáticas Fundamentales, UNED 28040 Madrid, Spain
Department of Mathematics, University of Auckland Private Bag 92109, Auckland, New Zealand

Received 13 June 1996. Revision received 3 June 1997.

The question of extendability of the action of a cyclic group of automorphisms of a compact Riemann surface is considered. Particular attention is paid to those cases corresponding to Singerman's list of Fuchsian groups which are not finitely-maximal, and more generally to cases involving a Fuchsian triangle group. The results provide partial answers to the question of which cyclic groups are the full automorphism group of some Riemann surface of given genus g>1.


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