Groups, Geometry, and Dynamics


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Volume 3, Issue 3, 2009, pp. 379–387
DOI: 10.4171/GGD/62

Published online: 2009-09-30

Square-free words as products of commutators

Andrew J. Duncan[1] and Alina Vdovina[2]

(1) University of Newcastle, Great Britain
(2) University of Newcastle, Great Britain

Elements of the commutator subgroup of a free group F can be presented as values of canonical forms, called Wicks forms. We show that, starting from sufficiently high genus g, there is a sequence of words wg which can be presented by f(g) distinct Wicks forms, where f(g) > g!. Moreover we may choose these words wg to be square-free.

Keywords: Commutators, free group, square-free words

Duncan Andrew, Vdovina Alina: Square-free words as products of commutators. Groups Geom. Dyn. 3 (2009), 379-387. doi: 10.4171/GGD/62