Kernels, inflations, evaluations, and imprimitivity of Mackey functors
Journal of Algebra
1993 - 2029
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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.
Faithful Mackey functor
Imprimitive Mackey functor
Projective Mackey functor
Published Version (Please cite this version)http://dx.doi.org/10.1016/j.jalgebra.2007.09.027
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