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

Jose L. Rodriguez·Antonio Viruel·Jerome Scherer
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Abstract

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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Jose L. Rodriguez, Antonio Viruel, Jerome Scherer. 2004-03-08. Preservation of perfectness and acyclicity; Berrick and Casacuberta's universal acyclic space localized at a set of primes. https://doi.org/10.1515/form.2005.17.1.67

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