Group varieties not closed under cellular covers and localizations

DOI10.1515/jgth-2017-0021zbMath1429.20021OpenAlexW2748841099MaRDI QIDQ1676212

Peng Zhang

Publication date: 6 November 2017

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jgth-2017-0021

zbMATH Keywords

variety of groupscellular coverlifting of homomorphismsBurnside groupTarski monstergroup localizationuniversal central cover

Mathematics Subject Classification ID

Periodic groups; locally finite groups (20F50) Simple groups (20E32) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Quasivarieties and varieties of groups (20E10)

Related Items (2)

Generators and closed classes of groups ⋮ On localizations of quasi-simple groups with given countable center

Cites Work

• Localizations of abelian Eilenberg-Mac Lane spaces of finite type
• Approximations and endomorphism algebras of modules. Volume 1: Approximations. Volume 2: Predictions.
• Group extensions, representations, and the Schur multiplicator
• Cellular covers of groups
• The \(A\)-core and \(A\)-cover of a group.
• Cellular covers of Abelian groups.
• A note on the localization of finite groups
• On cellular covers with free kernels.
• On kernels of cellular covers
• Cellular covers of totally ordered abelian groups
• CONSTRUCTING SIMPLE GROUPS FOR LOCALIZATIONS
• Large localizations of finite simple groups
• Cellular covers for R$R$-modules and varieties of groups
• Varieties of groups
• Uncountably many Varieties of Groups
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