On compactifications and product‐free sets
A subset of a group is said to be product free if it does not contain three elements satisfying the equation x·y=z. We give a negative answer to a question of Babai and Sós on the existence of large product-free sets in finite groups by model theoretic means. This question was originally answered by...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/98558 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/98558 |
| Access Level: | acceso abierto |
| Palabra clave: | Lógica simbólica y matemática (Matemáticas) 1102.10 Teoría de Modelos 1202.05 Análisis Combinatorio |
| Sumario: | A subset of a group is said to be product free if it does not contain three elements satisfying the equation x·y=z. We give a negative answer to a question of Babai and Sós on the existence of large product-free sets in finite groups by model theoretic means. This question was originally answered by Gowers. Furthermore, we give a natural and sufficient model theoretic condition for a group to have a large product-free subset, as well as a model theoretic account of a result of Nikolov and Pyber on triple products. |
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