Cellular covers of groups

Emmanuel Dror Farjoun, Rüdiger Göbel, Yoav Segev

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

In this paper we discuss the concept of cellular cover for groups, especially nilpotent and finite groups. A cellular cover is a group homomorphism c : G → M such that composition with c induces an isomorphism of sets between Hom (G, G) and Hom (G, M). An interesting example is when G is the universal central extension of the perfect group M. This concept originates in algebraic topology and homological algebra, where it is related to the study of localizations of spaces and other objects. As explained below, it is closely related to the concept of cellular approximation of any group by a given fixed group. We are particularly interested in properties of M that are inherited by G, and in some cases by properties of the kernel of the map c.

Original languageEnglish
Pages (from-to)61-76
Number of pages16
JournalJournal of Pure and Applied Algebra
Volume208
Issue number1
DOIs
StatePublished - 1 Jan 2007

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