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Groups Of Automorphisms Of Hyperelliptic Klein Surfaces Of Genus 3

Gamboa Mutuberria, José Manuel and Bujalance, E. and Etayo Gordejuela, J. Javier (1986) Groups Of Automorphisms Of Hyperelliptic Klein Surfaces Of Genus 3. Michigan Mathematical Journal, 33 . pp. 55-74. ISSN 0026-2285

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Abstract

The order of a group of automorphisms of a compact Klein surface of genus 3 with boundary does not exceed 24 [see C. L. May, Pac. J. Math. 59, 199-210 (1975; Zbl 0422.30037)]. These groups of automorphisms are quotients of NEC groups of isometries of the hyperbolic plane since the Klein surface may be represented as the quotient of the hyperbolic plane by an NEC group. Being hyperelliptic places certain restrictions on the possible signatures of the corresponding NEC groups. By an exhaustive search starting with the finite groups of order less than 24 and using a variety of structural results on NEC groups (several proved in earlier papers by one or more of these authors) those finite groups which can occur as the full group of automorphisms of a hyperelliptic Klein surface of genus 3 are precisely determined. The fullness is exhibited by a simple argument on dimensions of Teichm¨uller spaces.


Item Type:Article
Uncontrolled Keywords:group of automorphisms of a compact Klein surface of genus 3; quotients of NEC groups; isometries of the hyperbolic plane; Teichm¨uller spaces
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:15386
Deposited On:28 May 2012 08:49
Last Modified:06 Feb 2014 10:23

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