On uniform exponential growth for solvable groups

TL;DR

This paper proves that solvable groups exhibit uniform exponential growth using a ping-pong argument, discusses the phenomenon of slow exponential growth, and shows it vanishes in finite index subgroups.

Contribution

It provides a new proof of Osin's uniform exponential growth for solvable groups and analyzes the behavior of exponential growth in subgroups.

Findings

Proof of uniform exponential growth for solvable groups

Disappearance of slow exponential growth in finite index subgroups

Application of ping-pong technique to group growth

Abstract

Using a theorem of J. Groves we give a ping-pong proof of Osin's uniform exponential growth for solvable groups. We discuss slow exponential growth and show that this phenomenon disappears as one passes to a finite index subgroup.