JournalsggdVol. 3 , No. 3DOI 10.4171/ggd/62

Square-free words as products of commutators

  • Andrew J. Duncan

    University of Newcastle, Great Britain
  • Alina Vdovina

    University of Newcastle, Great Britain
Square-free words as products of commutators cover

Abstract

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.