Bounding the residual finiteness of free groups

Authors:
Martin Kassabov and Francesco Matucci

Journal:
Proc. Amer. Math. Soc. **139** (2011), 2281-2286

MSC (2010):
Primary 20F69; Secondary 20E05, 20E07, 20E26

Published electronically:
February 25, 2011

MathSciNet review:
2784792

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Abstract | References | Similar Articles | Additional Information

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 of length in non-abelian free groups with the property that is the identity on all finite quotients of size 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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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

Email:
fm6w@virginia.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-10967-5

Keywords:
Free group,
residually finite group,
identities in a group

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

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.