Bounding the residual finiteness of free groups

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Description/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 wn of length n in non-abelian free groups with the property that wn is the identity on all finite quotients of size ∼ n2/3 or less. This improves on a previous result of Bou- Rabee and McReynolds quantifying the lower bound of the residual finiteness of free groups.