Bounding the residual finiteness of free groups
Bounding the residual finiteness of free groups
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.
Kassabov, Martin
b78efbac-c468-4838-ac56-5f23181f595c
Matucci, Francesco
b4661e9d-c6e3-41b6-b545-400b77afc190
Kassabov, Martin
b78efbac-c468-4838-ac56-5f23181f595c
Matucci, Francesco
b4661e9d-c6e3-41b6-b545-400b77afc190
Kassabov, Martin and Matucci, Francesco
(2010)
Bounding the residual finiteness of free groups.
Pre-print.
(In Press)
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.
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Accepted/In Press date: December 2010
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Local EPrints ID: 155211
URI: http://eprints.soton.ac.uk/id/eprint/155211
PURE UUID: 8ef2a3ec-7942-417e-8002-f0580e6eda4f
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Date deposited: 28 May 2010 09:23
Last modified: 14 Mar 2024 01:37
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Author:
Martin Kassabov
Author:
Francesco Matucci
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