Geodesic
Square-free words as products of commutators
Andrew J. Duncan1 ; Alina Vdovina1 orcid
1University of Newcastle, Great Britain
Groups, geometry, and dynamics, Tome 3 (2009) no. 3, pp. 379-387

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DOI

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.
DOI : 10.4171/ggd/62
Classification : 20-XX, 00-XX
Mots-clés : Commutators, free group, square-free words

Andrew J. Duncan  1   ; Alina Vdovina  1

1 University of Newcastle, Great Britain 
Andrew J. Duncan; Alina Vdovina. Square-free words as products of commutators. Groups, geometry, and dynamics, Tome 3 (2009) no. 3, pp. 379-387. doi: 10.4171/ggd/62
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     doi = {10.4171/ggd/62},
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