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. © 2010 American Mathematical Society.
Kassabov, M., Matucci, F. (2011). Bounding the residual finiteness of free groups. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 139(7), 2281-2286 [10.1090/S0002-9939-2011-10967-5].
Bounding the residual finiteness of free groups
Matucci, F
2011
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. © 2010 American Mathematical Society.
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