On Freiman's Theorem in Nilpotent Groups

TL;DR

This paper generalizes Freiman's theorem, originally in additive combinatorics, to a broad class of nilpotent Lie groups, expanding its applicability beyond the Heisenberg group.

Contribution

It extends Tao's result on Freiman's theorem from the Heisenberg group to all simply connected nilpotent Lie groups of any step.

Findings

Generalization of Freiman's theorem to nilpotent Lie groups

Extension of Tao's results beyond the Heisenberg group

Broader understanding of additive structure in non-abelian groups

Abstract

We generalize a result of Tao which extends Freiman's theorem to the Heisenberg group. We extend it to simply connected nilpotent Lie groups of arbitrary step.