Bounding the residual finiteness of free groups
Martin Kassabov, Francesco Matucci · Proceedings of the American Mathematical Society · 2011
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 w_n of length n n in non-abelian free groups with the property that w n w_n is the identity on all finite quotients of size ∼ n 2 / 3 \sim 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.