Square-free words as products of commutators

  • Andrew J. Duncan

    University of Newcastle, Great Britain
  • Alina Vdovina

    University of Newcastle, Great Britain

Abstract

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

Cite this article

Andrew J. Duncan, Alina Vdovina, Square-free words as products of commutators. Groups Geom. Dyn. 3 (2009), no. 3, pp. 379–387

DOI 10.4171/GGD/62