On trivial words in finitely presented groups

M. Elder; A. Rechnitzer; E. J. Janse van Rensburg; T. Wong

On trivial words in finitely presented groups

Group Theory 2013-12-23 v3 Combinatorics Probability

Authors: M. Elder , A. Rechnitzer , E. J. Janse van Rensburg , T. Wong

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.

Keywords

combinatorial group theory group theory

Cite

@article{arxiv.1210.3425,
  title  = {On trivial words in finitely presented groups},
  author = {M. Elder and A. Rechnitzer and E. J. Janse van Rensburg and T. Wong},
  journal= {arXiv preprint arXiv:1210.3425},
  year   = {2013}
}

Comments

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

On trivial words in finitely presented groups

Abstract

Keywords

Cite

Comments

Related papers