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Cayley graphs of finitely generated groups
Author:
Simon Thomas
Journal:
Proc. Amer. Math. Soc. 134 (2006), 289-294
MSC (2000):
Primary 03E15, 20F05
Posted:
June 14, 2005
MathSciNet review:
2170570
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Abstract: There does not exist a Borel choice of generators for each finitely generated group which has the property that isomorphic groups are assigned isomorphic Cayley graphs.
References
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B. H. Bowditch, Continuously many quasiisometry classes of 2-generator groups, Comment. Math. Helv. 73 (1998), 232-236. MR 1611695 (99f:20062)
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C. Champetier, L'espace des groupes de type fini, Topology 39 (2000), 657-680. MR 1760424 (2001i:20084)
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P. de la Harpe, Topics in Geometric Group Theory, Chicago Lectures in Mathematics Series, The University of Chicago Press, Chicago, 2000. MR 1786869 (2001i:20081)
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R. M. Solovay, A model of set theory in which every set of reals is Lebesgue measurable, Ann. Math. 92 (1970), 1-56. MR 0265151 (42:64)
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S. Thomas, The virtual isomorphism problem for finitely generated groups, Bull. Lond. Math. Soc. 35 (2003), 777-784.MR 2000024 (2004g:03076)
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S. Thomas and B. Velickovic, On the complexity of the isomorphism relation for finitely generated groups, J. Algebra 217 (1999), 352-373.MR 1700491 (2000i:20001)
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Additional Information
Simon Thomas
Affiliation:
Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
Email:
sthomas@math.rutgers.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-05-07987-6
PII:
S 0002-9939(05)07987-6
Received by editor(s):
February 2, 2004
Received by editor(s) in revised form:
September 2, 2004
Posted:
June 14, 2005
Additional Notes:
This research was partially supported by NSF Grants.
Communicated by:
Carl G. Jockusch, Jr.
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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