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.
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Derek F. Holt, Garside groups have the falsification by fellow-traveller property. Groups Geom. Dyn. 4 (2010), no. 4, pp. 777–784DOI 10.4171/GGD/105