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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A non-residually solvable hyperlinear one-relator group


Author: Jon P. Bannon
Journal: Proc. Amer. Math. Soc. 139 (2011), 1409-1410
MSC (2010): Primary 46L10; Secondary 20F65
Published electronically: August 30, 2010
MathSciNet review: 2748433
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Abstract: In this short paper, we prove that the group $ \langle a,b\vert a=[a,a^{b}]\rangle$ is hyperlinear. Unlike the nonresidually finite Baumslag-Solitar groups, this group is not residually solvable.


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Jon P. Bannon
Affiliation: Department of Mathematics, Siena College, Loudonville, New York 12211
Email: jbannon@siena.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10668-8
PII: S 0002-9939(2010)10668-8
Keywords: Sofic group, hyperlinear group, one-relator group
Received by editor(s): February 17, 2010
Received by editor(s) in revised form: April 26, 2010
Published electronically: August 30, 2010
Communicated by: Marius Junge
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.