English

Bounding the residual finiteness of free groups

Group Theory 2011-05-19 v2

Abstract

We find a lower bound to the size of finite groups detecting a given word in the free group, more precisely we construct a word w_n of length n in non-abelian free groups with the property that w_n is the identity on all finite quotients of size ~ n^{2/3} or less. This improves on a previous result of Bou-Rabee and McReynolds quantifying the lower bound of the residual finiteness of free groups.

Keywords

Cite

@article{arxiv.0912.2368,
  title  = {Bounding the residual finiteness of free groups},
  author = {Martin Kassabov and Francesco Matucci},
  journal= {arXiv preprint arXiv:0912.2368},
  year   = {2011}
}

Comments

6 pages, no figures; final version