论文标题
概率类似的nilpotent组
Probabilistically-like nilpotent groups
论文作者
论文摘要
本文的主要目的是提出一个通用模型理论框架，以了解Shalev在概率有限的nilpotent组上的结果。我们证明，在模型理论意义上，方程$ [x_1，\ ldots，x_k] = 1 $保持的合适组是宽图的范围，这是一个小于$ k $的nilpotent class组的延伸，而小于$ k $，均为均匀的本地有限群体。特别是，该结果适用于正式的群体，以及可确定群体的合适模型理论家族，例如简单理论中的组和具有有限令人满意的仿制药的群体。
The 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 $[x_1,\ldots,x_k]=1$ 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.
