The falsification by fellow traveler property implies geodesic autostackability
Group Theory
2022-12-07 v2
Abstract
Groups with the falsification by fellow traveler property are known to have solvable word problem, but they are not known to be automatic or to have finite convergent rewriting systems. In this paper, we show that these groups admit a generalization of the two properties; namely, they are geodesically autostackable. As a key part of proving this, we show that a wider class of groups, namely groups with a weight non-increasing synchronously regular convergent prefix-rewriting system, have a bounded regular convergent prefix-rewriting system.
Keywords
Cite
@article{arxiv.2209.11912,
title = {The falsification by fellow traveler property implies geodesic autostackability},
author = {Ash DeClerk},
journal= {arXiv preprint arXiv:2209.11912},
year = {2022}
}
Comments
22 pages, 4 figures. Extended Theorem A to find autostackable structures for groups with weight non-increasing (as opposed to length non-increasing) CP-RSs, along with minor edits for typos and clarity