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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Detalles Bibliográficos
Autor: Palacín Cruz, Daniel
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
Descripción
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.