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A note on localizations of perfect groups
Author(s):
Bernard
Badzioch;
Mark
Feshbach
Journal:
Proc. Amer. Math. Soc.
133
(2005),
693-697.
MSC (2000):
Primary 20J15;
Secondary 55P60, 20F38
Posted:
September 29, 2004
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Additional information
Abstract:
We describe a perfect group whose localization is not perfect.
References:
-
- 1.
- Carles Casacuberta. On structures preserved by idempotent transformations of groups and homotopy types. In Crystallographic groups and their generalizations (Kortrijk,1999), volume 262 of Contemp. Math., pages 39-68. Amer. Math. Soc., Providence, RI, 2000. MR 1796125 (2001i:55012)
- 2.
- Assaf Libman. Cardinality and nilpotency of localizations of groups and
 -modules. Israel J. Math., 117:221-237, 2000. MR 1760593 (2001c:20107) - 3.
- Assaf Libman. A note on the localization of finite groups. J. Pure Appl. Algebra, 148(3):271-274, 2000. MR 1758733 (2001c:20108)
- 4.
- Wilhelm Magnus, Abraham Karrass, and Donald Solitar. Combinatorial group theory: Presentations of groups in terms of generators and relations. Interscience Publishers [John Wiley & Sons, Inc.], New York-London-Sydney, 1966. MR 0207802 (34:7617)
- 5.
- Niamh O'Sullivan. Localizations of free soluble groups. J. Group Theory, 4(1):89-96, 2001. MR 1808841 (2001k:20070)
- 6.
- Jean-Pierre Serre. Trees. Springer-Verlag, Berlin, 1980. MR 0607504 (82c:20083)
- 7.
- José L. Rodríguez, Jérôme Scherer and Antonio Viruel, Preservation of perfectness and acyclicity: Berrick and Casacuberta's universal acyclic space localized at a set of primes. Forum Mathematicum, to appear.
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Additional Information:
Bernard
Badzioch
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email:
badzioch@math.umn.edu
Mark
Feshbach
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email:
feshbach@math.umn.edu
DOI:
10.1090/S0002-9939-04-07562-8
PII:
S 0002-9939(04)07562-8
Received by editor(s):
January 10, 2003
Received by editor(s) in revised form:
November 9, 2003
Posted:
September 29, 2004
Communicated by:
Paul Goerss
Copyright of article:
Copyright
2004,
American Mathematical Society
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