On trivial words in finitely presented groups

2012/10/12 by M. Elder, Elder, M., A. Rechnitzer +5 · 2 citations
Mathematics · #05A15 #20F69 #60J20 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR) #math.CO #math.GR #math.PR #msc:05A15 #msc:20F69 #msc:60J20

paper · pdf · doi:10.48550/arxiv.1210.3425

This article has been rewritten as two separate papers, with improved exposition. The new papers are arXiv:1309.4184 and arXiv:1312.5722

arxiv created 2013/12/20 · arxiv updated 2013/12/23

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 BS(N,N) = < a,b | a^N b = b a^N > and prove that their cogrowth rates are algebraic numbers.

Citations

• Random sampling of trivials words in finitely presented groups

Cited by

• Random sampling of trivials words in finitely presented groups
• The cogrowth series for BS(N,N) is D-finite

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