Dyer groups have the falsification by fellow-traveller property
Group Theory
2026-02-23 v1
Abstract
This paper is devoted to the study of the falsification by fellow-traveller property (FFTP) in Dyer groups. We exhibit a finite generating set for which the associated Cayley graph is a locally finite mediangle graph, and leverage its properties to prove that Dyer groups have the FFTP. It follows that Dyer groups have finitely many cone types, emphasising their role in providing a unified approach to Coxeter groups and graph products of cyclic groups.
Keywords
Cite
@article{arxiv.2602.18220,
title = {Dyer groups have the falsification by fellow-traveller property},
author = {Megan Howarth},
journal= {arXiv preprint arXiv:2602.18220},
year = {2026}
}
Comments
20 pages, 11 figures. Comments are welcome!