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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Bounding the residual finiteness of free groups
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by Martin Kassabov and Francesco Matucci PDF
Proc. Amer. Math. Soc. 139 (2011), 2281-2286 Request permission

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 $\sim n^{2/3}$ or less. This improves on a previous result of Bou-Rabee and McReynolds quantifying the lower bound of the residual finiteness of free groups.
References
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Additional Information
  • Martin Kassabov
  • Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
  • Address at time of publication: School of Mathematics, University of Southampton, University Road, Southampton, SO17 1BJ, United Kingdom
  • Email: kassabov@math.cornell.edu
  • Francesco Matucci
  • Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
  • MR Author ID: 788744
  • Email: fm6w@virginia.edu
  • Received by editor(s): March 3, 2010
  • Published electronically: February 25, 2011
  • Additional Notes: The first author was partially funded by National Science Foundation grants DMS 0600244, 0635607 and 0900932.
  • Communicated by: Jonathan I. Hall
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 2281-2286
  • MSC (2010): Primary 20F69; Secondary 20E05, 20E07, 20E26
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10967-5
  • MathSciNet review: 2784792