论文标题
具有有限的VC维度的近似亚组
Approximate subgroups with bounded VC-dimension
论文作者
论文摘要
We combine the fundamental results of Breuillard, Green, and Tao on the structure of approximate groups, together with "tame" arithmetic regularity methods based on work of the authors and Terry, to give a structure theorem for finite subsets $A$ of arbitrary groups $G$ where $A$ has "small tripling" and bounded VC-dimension: Roughly speaking, up to a small error, $A$ will be a union of a bounded number of翻译有界等级和步骤的coset nilprogression（请参见定理2.1）。我们还证明了在有界指数的设置中获得更强的结果（请参见定理2.2）。我们的结果扩大了Martin-Pizarro，Palacín和Wolf的最新工作，并在有限的稳定稳定套件上进行了三倍的三倍。
We combine the fundamental results of Breuillard, Green, and Tao on the structure of approximate groups, together with "tame" arithmetic regularity methods based on work of the authors and Terry, to give a structure theorem for finite subsets $A$ of arbitrary groups $G$ where $A$ has "small tripling" and bounded VC-dimension: Roughly speaking, up to a small error, $A$ will be a union of a bounded number of translates of a coset nilprogression of bounded rank and step (see Theorem 2.1). We also prove a stronger result in the setting of bounded exponent (see Theorem 2.2). Our results extend recent work of Martin-Pizarro, Palacín, and Wolf on finite stable sets of small tripling.
