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Cayley graphs of finitely generated groups
Author(s):
Simon
Thomas
Journal:
Proc. Amer. Math. Soc.
134
(2006),
289-294.
MSC (2000):
Primary 03E15, 20F05
Posted:
June 14, 2005
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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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- 1.
- B. H. Bowditch, Continuously many quasiisometry classes of 2-generator groups, Comment. Math. Helv. 73 (1998), 232-236. MR 1611695 (99f:20062)
- 2.
- C. Champetier, L'espace des groupes de type fini, Topology 39 (2000), 657-680. MR 1760424 (2001i:20084)
- 3.
- 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)
- 4.
- G. Hjorth and A. S. Kechris, Borel equivalence relations and classification of countable models, Ann. Pure Appl. Logic 82 (1996), 221-272. MR 1423420 (99m:03073)
- 5.
- R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Springer-Verlag, 1977. MR 0577064 (58:28182)
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- 7.
- S. Thomas, The virtual isomorphism problem for finitely generated groups, Bull. Lond. Math. Soc. 35 (2003), 777-784.MR 2000024 (2004g:03076)
- 8.
- 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:
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.
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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