Palacín Cruz, Daniel2024-02-032024-02-032022D. Palacín, Probabilistically-like nilpotent groups, Journal of Algebra 606 (2022) 798–818. https://doi.org/10.1016/j.jalgebra.2022.05.010.0021-869310.1016/j.jalgebra.2022.05.010https://hdl.handle.net/20.500.14352/98553The main goal of the paper is to present a general model theoretic framework to understand a result of Shalev on probabilistically finite nilpotent groups. We prove that a suitable group where the equation [x_1,...,x_k]=1 holds on a wide set, in a model theoretic sense, is an extension of a nilpotent group of class less than k by a uniformly locally finite group. In particular, this result applies to amenable groups, as well as to suitable model-theoretic families of definable groups such as groups in simple theories and groups with finitely satisfiable generics.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articlehttps://doi.org/10.1016/j.jalgebra.2022.05.010restricted accessLógica simbólica y matemática (Matemáticas)Grupos (Matemáticas)1102.10 Teoría de Modelos1201.06 Grupos, Generalidades