The falsification by fellow traveler property implies geodesic autostackability

TL;DR

This paper demonstrates that groups with the falsification by fellow traveler property are geodesically autostackable, broadening understanding of their algebraic structure and computational properties.

Contribution

It establishes that such groups admit a generalized form of autostackability, connecting their properties to convergent prefix-rewriting systems.

Findings

Groups with the falsification by fellow traveler property are geodesically autostackable.

Wider classes of groups with specific rewriting systems have bounded regular convergent prefix-rewriting systems.

The results link algebraic properties with computational rewriting system frameworks.

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.