Centralizers in pseudo-finite groups
The role of finite centralizers of involutions in pseudo-finite groups is analyzed. It is shown that a pseudo-finite group admitting a definable involutory automorphism fixing only finitely many elements is finite-by-abelian-by-finite. As a consequence, we give a model-theoretic proof of a result fo...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/98546 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/98546 |
| Access Level: | acceso abierto |
| Palabra clave: | Lógica simbólica y matemática (Matemáticas) Grupos (Matemáticas) 1102.10 Teoría de Modelos 1201.06 Grupos, Generalidades |
| Sumario: | The role of finite centralizers of involutions in pseudo-finite groups is analyzed. It is shown that a pseudo-finite group admitting a definable involutory automorphism fixing only finitely many elements is finite-by-abelian-by-finite. As a consequence, we give a model-theoretic proof of a result for periodic groups due to Hartley and Meixner. Furthermore, it is shown that any pseudo-finite group has an infinite abelian subgroup. |
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