Bounding the residual finiteness of free groups

Details Bounding the residual finiteness of free groups Bounding the residual finiteness of free groups

2009-12-11

arxiv.org/abs/0912.2368v2

Proceedings of the American Mathematical Society 139 (2011), no. 7, 2281-2286

Mathematics

Group Theory

6 pages, no figures; final version

Scientific paper

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.

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