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On trivial words in finitely presented groups

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arxiv 1210.3425 v3 pith:JIFM6GTK submitted 2012-10-12 math.GR math.COmath.PR

M. Elder , A. Rechnitzer , E. J. Janse van Rensburg , T. Wong This is my paper
classification math.GRmath.COmath.PR
keywords groupscogrowthfinitelynumericalpresentedseriesalgebraicbaumslag-solitar
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abstract

We propose a numerical method for studying the cogrowth of finitely presented groups. To validate our numerical results we compare them against the corresponding data from groups whose cogrowth series are known exactly. Further, we add to the set of such groups by finding the cogrowth series for Baumslag-Solitar groups $\mathrm{BS}(N,N) = < a,b | a^N b = b a^N >$ and prove that their cogrowth rates are algebraic numbers.

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