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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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