Preservation of perfectness and acyclicity; Berrick and Casacuberta's universal acyclic space localized at a set of primes

Details Preservation of perfectness and acyclicity; Berrick and Casacuberta's universal acyclic space localized at a set of primes Preservation of perfectness and acyclicity; Berrick and Casacuberta's universal acyclic space localized at a set of primes

2003-01-28

arxiv.org/abs/math/0301325v2

Forum Math. 17 (2005), no. 1, 67--75.

Mathematics

Group Theory

11 pages. To appear in Forum Mathematicum

Scientific paper

10.1515/form.2005.17.1.67

In this paper we answer negatively a question posed by Casacuberta, Farjoun, and Libman about the preservation of perfect groups under localization functors. Indeed, we show that a certain $P$-localization of Berrick and Casacuberta's universal acyclic group is not perfect. We also investigate under which conditions perfectness is preserved: For instance, we show that if the localization of a perfect group is finite then it is perfect.

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