Preservation of Perfectness and Acyclicity: Berrick and Casacuberta's Universal Acyclic Space Localized at a Set of Primes

DOI10.1515/FORM.2005.17.1.67zbMATH Open1070.55005arXivmath/0301325OpenAlexW3101460017MaRDI QIDQ4661826

Author name not available (Why is that?)

Publication date: 30 March 2005

Published in: Forum Mathematicum (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/math/0301325

zbMATH Keywords

localizationperfect group

Mathematics Subject Classification ID

Localization and completion in homotopy theory (55P60) Other groups related to topology or analysis (20F38) Residual properties and generalizations; residually finite groups (20E26) Category of groups (20J15)

Related Items (7)

Large localizations of finite groups. ⋮ Non-simple localizations of finite simple groups. ⋮ A note on localizations of perfect groups ⋮ On the cokernel of the Baumslag rationalization ⋮ On localizations of quasi-simple groups with given countable center ⋮ Right exact localizations of groups ⋮ Title not available (Why is that?)

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