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