Preprint

On infinite discrete approximate subgroups in Rd

Alexander Fish


Abstract

In this paper we show that any discrete, infinite approximate subgroup ΛRd is relatively dense around some linear subspace LRd, i.e., there exists R>0 such that for every ball BR(x) with center at xL we have ΛBR(x), and ΛxLBR(x). As an application of our main theorem, we provide a complete classification of infinite approximate subgroups in Zd.

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Thursday, March 8, 2018