Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The classification of torsion-free abelian groups of finite rank up to isomorphism and up to quasi-isomorphism

Author: Samuel Coskey
Journal: Trans. Amer. Math. Soc. 364 (2012), 175-194
MSC (2010): Primary 03E15; Secondary 20K15
Published electronically: August 31, 2011
MathSciNet review: 2833581
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The isomorphism and quasi-isomorphism relations on the $p$-local torsion-free abelian groups of rank $n\geq 3$ are incomparable with respect to Borel reducibility.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 03E15, 20K15

Retrieve articles in all journals with MSC (2010): 03E15, 20K15

Additional Information

Samuel Coskey
Affiliation: Mathematics Program, The Graduate Center of The City University of New York, 365 Fifth Avenue, New York, New York 10016
Address at time of publication: York University and The Fields Institute, 222 College Street, Toronto, Ontario, Canada M5S 2N2

Keywords: Countable Borel equivalence relations, torsion-free abelian groups, superrigidity
Received by editor(s): February 6, 2009
Received by editor(s) in revised form: March 16, 2010
Published electronically: August 31, 2011
Additional Notes: This is a part of the author’s doctoral thesis, which was written under the supervision of Simon Thomas. This work was partially supported by NSF grant DMS 0600940.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.