Abstract
Skeletal signatures were introduced in Anderson and Wootton (see [1]) as a tool to describe the space of all signatures with which a group can act on a surface of genus σ ≥ 2. In the present paper, we provide an essentially complete description of the regular gaps that appear in the space of skeletal signatures, together with proofs of those parts of the conjectures posed in Anderson and Wootton (see [1]) related to these regular gaps.
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Anderson J.W., Wootton A.: A Lower Bound for the Number of Group Actions on a Compact Riemann Surface, Algebr. Geom. Topol. 12, 19–35 (2012)
T. Breuer, Characters and Automorphism Groups of Compact Riemann Surfaces, London Mathematical Society Lecture Note Series 280, Cambridge University Press (2001).
Broughton S.A.: Classifying Finite Group Actions on Surfaces of Low Genus, J. Pure Appl. Algebra 69, 233–270 (1990)
The GAP Group. GAP - Groups, Algorithms and Programming, Version 4.4, 2006 (http://www.gap-system.org)
Guralnick R.: On the number of generators of a finite group, Arch. Math. 53, 521–523 (1989)
Harvey W.J.: Cyclic groups of automorphisms of a compact Riemann surface, Quart. J. Math. Oxford 17, 86–97 (1966)
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This work was supported in part by EPSRC grant EP/K033239/1. Both authors would like to thanks the other’s institution for its hospitality during the work that led to this paper.
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Anderson, J.W., Wootton, A. Gaps in the space of skeletal signatures. Arch. Math. 102, 181–190 (2014). https://doi.org/10.1007/s00013-014-0607-7
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DOI: https://doi.org/10.1007/s00013-014-0607-7