Tubular free by cyclic groups and the strongest Tits alternative
Group Theory
2015-10-21 v1 Geometric Topology
Abstract
We show, using Wise's equitable sets criterion, that every tubular free by cyclic group acts freely on a CAT(0) cube complex. We also show that these groups have a finite index subgroup satisfying the strongest Tits alternative, which means that every subgroup either surjects a non abelian free group or is torsion free abelian. In particular the Gersten group is the first known group virtually having this property but which is not virtually special nor virtually residually free.
Keywords
Cite
@article{arxiv.1510.05842,
title = {Tubular free by cyclic groups and the strongest Tits alternative},
author = {J. O. Button},
journal= {arXiv preprint arXiv:1510.05842},
year = {2015}
}