Groups, Geometry, and Dynamics


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Volume 4, Issue 4, 2010, pp. 777–784
DOI: 10.4171/GGD/105

Published online: 2010-10-15

Garside groups have the falsification by fellow-traveller property

Derek F. Holt[1]

(1) University of Warwick, Coventry, United Kingdom

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

Keywords: Garside groups, braid groups, Artin groups, geodesics, regular sets, fellow-traveller property

Holt Derek: Garside groups have the falsification by fellow-traveller property. Groups Geom. Dyn. 4 (2010), 777-784. doi: 10.4171/GGD/105