A note on localizations of perfect groups

A note on localizations of perfect groups
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by Bernard Badzioch and Mark Feshbach PDF

Proc. Amer. Math. Soc. 133 (2005), 693-697 Request permission

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.