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 ∪ X−1 K-fellow-travel with G-equivalent shorter words. This implies, in particular, that the set of all geodesic words over X ∪ X−1 is regular. We show that Garside groups with appropriate generating set satisfy FFTP.