Uniform Exponential Growth of Polycyclic Groups

TL;DR

This paper proves that polycyclic groups exhibit either polynomial growth or uniform exponential growth, establishing a clear dichotomy in their growth behavior.

Contribution

It is the first to establish a definitive dichotomy in the growth types of polycyclic groups, showing they are either polynomial or uniformly exponentially growing.

Findings

Polycyclic groups are either polynomial or uniformly exponentially growing.

The growth type is determined for all polycyclic groups.

Provides a complete classification of growth behaviors in this class.

Abstract

We prove that polycyclic groups are of polynomial growth or of uniform exponential growth.