A new proof of Gromov's theorem on groups of polynomial growth

TL;DR

This paper presents a novel proof of Gromov's theorem, demonstrating that finitely generated groups with polynomial growth contain a finite index nilpotent subgroup, avoiding the use of classical structure theory.

Contribution

It introduces a new proof technique for Gromov's theorem that bypasses the Montgomery-Zippin-Yamabe structure theory of locally compact groups.

Findings

Finitely generated groups of polynomial growth have a finite index nilpotent subgroup.

The new proof simplifies the understanding of Gromov's theorem.

Avoids reliance on classical structure theory methods.

Abstract

We give a new proof of Gromov's theorem that any finitely generated group of polynomial growth has a finite index nilpotent subgroup. Unlike the original proof, it does not rely on the Montgomery-Zippin-Yamabe structure theory of locally compact groups.