On extendability of group actions on compact Riemann surfaces

Bujalance, Emilio; Cirre, F.; Conder, Marston

doi:10.1090/S0002-9947-02-03184-7

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.

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