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dc.contributor.authorPakianathan, J.en_US
dc.contributor.authorYalçın, E.en_US
dc.date.accessioned2015-07-28T11:58:05Z
dc.date.available2015-07-28T11:58:05Z
dc.date.issued2007en_US
dc.identifier.issn0002-9947
dc.identifier.urihttp://hdl.handle.net/11693/11570
dc.description.abstractLet E be a central extension of the form 0 → V → G → W → 0 where V and W are elementary abelian 2-groups. Associated to E there is a quadratic map Q: W → V, given by the 2-power map, which uniquely determines the extension. This quadratic map also determines the extension class q of the extension in H2(W, V) and an ideal I(q) in H2(G, ℤ/2) which is generated by the components of q. We say that E is Bockstein closed if I(q) is an ideal closed under the Bockstein operator. We find a direct condition on the quadratic map Q that characterizes when the extension is Bockstein closed. Using this characterization, we show for example that quadratic maps induced from the fundamental quadratic map Qgln: gln(F2) → gln(F2) given by Q(A) = A + A2 yield Bockstein closed extensions. On the other hand, it is well known that an extension is Bockstein closed if and only if it lifts to an extension 0 → M → G̃ → W → 0 for some ℤ/4[W]-lattice M. In this situation, one may write β(q) = Lq for a "binding matrix" L with entries in H1(W, ℤ/2). We find a direct way to calculate the module structure of M in terms of L. Using this, we study extensions where the lattice M is diagonalizable/triangulable and find interesting equivalent conditions to these properties. © 2007 American Mathematical Society.en_US
dc.language.isoEnglishen_US
dc.source.titleTransactions of the American Mathematical Societyen_US
dc.relation.isversionofhttp://dx.doi.org/10.1090/S0002-9947-99-02470-8en_US
dc.titleQuadratic maps and Bockstein closed group extensionsen_US
dc.typeArticleen_US
dc.departmentDepartment of Mathematicsen_US
dc.citation.spage6079en_US
dc.citation.epage6110en_US
dc.citation.volumeNumber359en_US
dc.citation.issueNumber12en_US
dc.identifier.doi10.1090/S0002-9947-99-02470-8en_US
dc.publisherAmerican Mathematical Societyen_US
dc.identifier.eissn1088-6850


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