Some free-by-cyclic groups

TL;DR

This paper constructs specific free-by-cyclic groups that contain complex subgroups and are not subgroup separable, using Morse theory to analyze their properties.

Contribution

It introduces free-by-cyclic groups with non-free locally-free subgroups and demonstrates their non-subgroup separability using Morse theory.

Findings

Existence of free-by-cyclic groups with non-free locally-free subgroups

Examples of hyperbolic free-by-cyclic groups

Proof that these groups are not subgroup separable

Abstract

We exhibit free-by-cyclic groups containing non-free locally-free subgroups, including some word hyperbolic examples. We also show that these groups are not subgroup separable. We use Bestvina-Brady Morse theory in our arguments.