Kernels, inflations, evaluations, and imprimitivity of Mackey functors

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dc.citation.epage2029en_US
dc.citation.issueNumber5en_US
dc.citation.spage1993en_US
dc.citation.volumeNumber319en_US
dc.contributor.authorYaraneri, E.en_US
dc.date.accessioned2015-07-28T11:58:15Z
dc.date.available2015-07-28T11:58:15Z
dc.date.issued2008-03-01en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractLet M be a Mackey functor for a finite group G. By the kernel of M we mean the largest normal subgroup N of G such that M can be inflated from a Mackey functor for G / N. We first study kernels of Mackey functors, and (relative) projectivity of inflated Mackey functors. For a normal subgroup N of G, denoting by PH, VG the projective cover of a simple Mackey functor for G of the form SH, VG we next try to answer the question: how are the Mackey functors PH / N, VG / N and PH, VG related? We then study imprimitive Mackey functors by which we mean Mackey functors for G induced from Mackey functors for proper subgroups of G. We obtain some results about imprimitive Mackey functors of the form PH, VG, including a Mackey functor version of Fong's theorem on induced modules of modular group algebras of p-solvable groups. Aiming to characterize subgroups H of G for which the module PH, VG (H) is the projective cover of the simple K over(N, -)G (H)-module V where the coefficient ring K is a field, we finally study evaluations of Mackey functors. © 2007 Elsevier Inc. All rights reserved.en_US
dc.description.provenanceMade available in DSpace on 2015-07-28T11:58:15Z (GMT). No. of bitstreams: 1 10.1016-j.jalgebra.2007.09.027.pdf: 315363 bytes, checksum: cd36469ef460ea6d0bf6d583763dcbf7 (MD5)en
dc.identifier.doi10.1016/j.jalgebra.2007.09.027en_US
dc.identifier.eissn1090-266X
dc.identifier.issn0021-8693
dc.identifier.urihttp://hdl.handle.net/11693/11653
dc.language.isoEnglishen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.jalgebra.2007.09.027en_US
dc.source.titleJournal of Algebraen_US
dc.subjectEvaluationen_US
dc.subjectFaithful Mackey functoren_US
dc.subjectFong's theoremen_US
dc.subjectImprimitive Mackey functoren_US
dc.subjectInductionen_US
dc.subjectInflationen_US
dc.subjectKernelen_US
dc.subjectMackey algebraen_US
dc.subjectMackey functoren_US
dc.subjectProjective Mackey functoren_US
dc.titleKernels, inflations, evaluations, and imprimitivity of Mackey functorsen_US
dc.typeArticleen_US

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