Free by cyclic groups are large

TL;DR

The paper proves that groups formed by a free group of rank at least two extended by Z are large, using recent theorems and earlier results to establish this property.

Contribution

It demonstrates that free-by-Z groups are large by combining recent theorems with previous findings, providing a new proof of this property.

Findings

Free-by-Z groups are large.

The proof combines recent theorems with earlier results.

The approach simplifies understanding of largeness in these groups.

Abstract

If F is a free group of finite rank at least two then any group of the form F by Z is large. In this short note we show how this statement follows by combining a very recent theorem of Hagen and Wise (using work of Agol and of Wise) with earlier results of the author.