Realizing regular representations of finite groups
Given a regular representation of a finite group G and a positive integer number n, we construct a (finite) topological space X such that its group of homotopy classes of selfhomotopy equivalences E(X) and its group of homeomorphisms Aut(X) are isomorphic to G, and the action of G on the n-th homolo...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad Rey Juan Carlos |
| Repositorio: | BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos |
| OAI Identifier: | oai:burjcdigital.urjc.es:10115/40177 |
| Acceso en línea: | https://hdl.handle.net/10115/40177 |
| Access Level: | acceso abierto |
| Palabra clave: | finite topological spaces finite posets group of automorphisms homology groups representation of finite groups |
| Sumario: | Given a regular representation of a finite group G and a positive integer number n, we construct a (finite) topological space X such that its group of homotopy classes of selfhomotopy equivalences E(X) and its group of homeomorphisms Aut(X) are isomorphic to G, and the action of G on the n-th homology group Hn(X) is the regular representation. We also discuss other representations |
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