Garside groups have the falsification by fellow-traveller property

Abstract

A group $G$ is said to have the falsification by fellow-traveller property (FFTP) with respect to a specified finite generating set $X$ if, for some constant $K$, all non-geodesic words over $X\cup X^{-1}K$-fellow-travel with $G$-equivalent shorter words. This implies, in particular, that the set of all geodesic words over $X\cup X^{-1}$ is regular. We show that Garside groups with appropriate generating set satisfy FFTP.