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Square-free words as products of commutators

Lookup NU author(s): Dr Andrew Duncan, Dr Alina Vdovina

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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 w(g) which can be presented by f(g) distinct Wicks forms, where f(g) > g!. Moreover we may choose these words w(g) to be square-free.

Publication metadata

Author(s): Duncan A, Vdovina A

Publication type: Article

Publication status: Published

Journal: Groups, Geometry, and Dynamics

Year: 2009

Volume: 3

Issue: 3

Pages: 379-387

Date deposited: 27/11/2012

ISSN (print): 1661-7207

ISSN (electronic): 1661-7215

Publisher: European Mathematical Society Publishing House

URL: http://dx.doi.org/10.4171/GGD/62

DOI: 10.4171/GGD/62

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