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      Kernels, inflations, evaluations, and imprimitivity of Mackey functors

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      Author(s)
      Yaraneri, E.
      Date
      2008-03-01
      Source Title
      Journal of Algebra
      Print ISSN
      0021-8693
      Electronic ISSN
      1090-266X
      Publisher
      Elsevier
      Volume
      319
      Issue
      5
      Pages
      1993 - 2029
      Language
      English
      Type
      Article
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      Abstract
      Let 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.
      Keywords
      Evaluation
      Faithful Mackey functor
      Fong's theorem
      Imprimitive Mackey functor
      Induction
      Inflation
      Kernel
      Mackey algebra
      Mackey functor
      Projective Mackey functor
      Permalink
      http://hdl.handle.net/11693/11653
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.jalgebra.2007.09.027
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      • Department of Mathematics 653
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