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

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.

11 pages. To appear in Forum Mathematicum

Cited by in corpus (2)

• Non-simple localizations of finite simple groups
• Right exact localizations of groups