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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Detalles Bibliográficos
Autor: Chocano, Pedro J.
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
Descripción
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