Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/103920
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dc.titlePerfect radicals and homology of group extensions
dc.contributor.authorBerrick, A.J.
dc.contributor.authorHartley, B.
dc.date.accessioned2014-10-28T02:43:05Z
dc.date.available2014-10-28T02:43:05Z
dc.date.issued1987-03
dc.identifier.citationBerrick, A.J.,Hartley, B. (1987-03). Perfect radicals and homology of group extensions. Topology and its Applications 25 (2) : 165-173. ScholarBank@NUS Repository.
dc.identifier.issn01668641
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/103920
dc.description.abstractA group epimorphism Q:G↠Q preserves perfect radicals if φ{symbol}PG =PQ, where PG, PQ is maximal perfect in G, Q respectively. The following two questions are considered. Question 1. If Pπ1(B) acts trivially on H*(F;Z), does the fibration F→E{A figure is presented}B then have π1(p)(Pπ1(E)) = Pπ1(B)? Question 2. If {cauchy integral}:X→Y is a map of spaces which induces an isomorphism of homology groups, is π1(X){A figure is presented} π1(Y) Pπ1(Y) then an epimorphism? It is shown that each question is equivalent to its group-theoretic counterpart obtained when the spaces involved are classifying spaces of discrete groups. It is also shown that an affirmative answer to the second question implies an affirmative answer to Question 1. By means of a direct product construction on finite nilpotent groups a continuum of examples is exhibited to resolve these question in the negative. This leaves to an example of an inclusion map of a locally finite p-group in a countable hypoabelian group which induces an isomorphism of all homology groups. © 1987.
dc.sourceScopus
dc.typeArticle
dc.contributor.departmentMATHEMATICS
dc.description.sourcetitleTopology and its Applications
dc.description.volume25
dc.description.issue2
dc.description.page165-173
dc.description.codenTIAPD
dc.identifier.isiutNOT_IN_WOS
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