Virtually free-by-cyclic groups

Last month I blogged about coherent groups (i.e. groups whose finitely generated subgroups are finitely presented). There I also referred to an article of Daniel Wise about coherent groups that contains many open problems at the end. One of these problems is whether every one-relator group is coherent (a question posed by Baumslag in the 70s).

`Recently’ it was proven by Louder and Wilton that one-relator groups with torsion are coherent (arXiv:1805.11976). Two weeks ago this was strengthened by Kielak and Linton (arXiv:2302.11500) who proved that one-relator groups with torsion are virtually free-by-cyclic (which is a much stronger result since it clarifies the structure of such groups and coherence is then just a corollary).