A note on localizations of perfect groups
HTML articles powered by AMS MathViewer
- by Bernard Badzioch and Mark Feshbach PDF
- Proc. Amer. Math. Soc. 133 (2005), 693-697 Request permission
Abstract:
We describe a perfect group whose localization is not perfect.References
- Carles Casacuberta, On structures preserved by idempotent transformations of groups and homotopy types, Crystallographic groups and their generalizations (Kortrijk, 1999) Contemp. Math., vol. 262, Amer. Math. Soc., Providence, RI, 2000, pp. 39–68. MR 1796125, DOI 10.1090/conm/262/04167
- Assaf Libman, Cardinality and nilpotency of localizations of groups and $G$-modules, Israel J. Math. 117 (2000), 221–237. MR 1760593, DOI 10.1007/BF02773571
- Assaf Libman, A note on the localization of finite groups, J. Pure Appl. Algebra 148 (2000), no. 3, 271–274. MR 1758733, DOI 10.1016/S0022-4049(00)00019-0
- Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Interscience Publishers [John Wiley & Sons], New York-London-Sydney, 1966. MR 0207802
- Niamh O’Sullivan, Localizations of free soluble groups, J. Group Theory 4 (2001), no. 1, 89–96. MR 1808841, DOI 10.1515/jgth.2001.010
- Jean-Pierre Serre, Trees, Springer-Verlag, Berlin-New York, 1980. Translated from the French by John Stillwell. MR 607504
- 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.
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
- Received by editor(s): January 10, 2003
- Received by editor(s) in revised form: November 9, 2003
- Published electronically: September 29, 2004
- Communicated by: Paul Goerss
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 693-697
- MSC (2000): Primary 20J15; Secondary 55P60, 20F38
- DOI: https://doi.org/10.1090/S0002-9939-04-07562-8
- MathSciNet review: 2113917