Square free words as products of commutators

Details Square free words as products of commutators Square free words as products of commutators

2008-09-09

arxiv.org/abs/0809.1577v1

Mathematics

Group Theory

9 pages, 4 figures

Scientific paper

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 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.

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