  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.
