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arXiv · 0912.2368

Bounding the residual finiteness of free groups

Martin Kassabov·Francesco Matucci
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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.

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Martin Kassabov, Francesco Matucci. 2011-05-18. Bounding the residual finiteness of free groups. https://arxiv.org/abs/0912.2368

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