Groups Of Automorphisms Of Hyperelliptic Klein Surfaces Of Genus 3
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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1986 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/64625 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/64625 |
| Access Level: | acceso abierto |
| Palabra clave: | 512.7 Group of automorphisms of a compact Klein surface of genus 3 Quotients of NEC groups Isometries of the hyperbolic plane Teichm¨uller spaces Geometria algebraica 1201.01 Geometría Algebraica |
| Sumario: | 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. |
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