Full automorphism groups of large order of compact bordered Klein surfaces
Let S be a compact bordered Klein surface of algebraic genus g ≥ 2, and Aut(S) its full group of automorphisms, which is known to have order at most 12(g − 1). In this paper we consider groups G of automorphisms of order at least 4(g − 1) acting on such surfaces, and study whether G is the full grou...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Nacional de Educación a Distancia |
| Repositorio: | e-spacio. Repositorio Institucional de la UNED |
| Idioma: | inglés |
| OAI Identifier: | oai:e-spacio.uned.es:20.500.14468/23862 |
| Acceso en línea: | https://hdl.handle.net/20.500.14468/23862 |
| Access Level: | acceso abierto |
| Palabra clave: | 12 Matemáticas Groups of automorphisms Klein surfaces Extendability of group actions |
| Sumario: | Let S be a compact bordered Klein surface of algebraic genus g ≥ 2, and Aut(S) its full group of automorphisms, which is known to have order at most 12(g − 1). In this paper we consider groups G of automorphisms of order at least 4(g − 1) acting on such surfaces, and study whether G is the full group Aut(S) or, on the contrary, the action of G extends to a larger group. The extendability of the action depends first on the NEC signature with which G acts and, in some cases, also on whether a monodromy presentation of G admits or not a particular automorphism. For each signature we study which of the three possibilities [Aut(S) : G] = 1, 2 or 3 occur, and show that, whenever a possibility occurs, it occurs for infinitely many values of g. We find infinite families of groups G, explicitly described by generators and relations, which satisfy the corresponding equality. |
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