Browsing by Subject "Mackey algebra"

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    Kernels, inflations, evaluations, and imprimitivity of Mackey functors
    (Elsevier, 2008-03-01) Yaraneri, E.
    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.
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    Socles and radicals of Mackey functors
    (2009) Yaraneri, E.
    We study the socle and the radical of a Mackey functor M for a finite group G over a field K (usually, of characteristic p > 0). For a subgroup H of G, we construct bijections between some classes of the simple subfunctors of M and some classes of the simple K over(N, -)G (H)-submodules of M (H). We relate the multiplicity of a simple Mackey functor SH, V G in the socle of M to the multiplicity of V in the socle of a certain K over(N, -)G (H)-submodule of M (H). We also obtain similar results for the maximal subfunctors of M. We then apply these general results to some special Mackey functors for G, including the functors obtained by inducing or restricting a simple Mackey functor, Mackey functors for a p-group, the fixed point functor, and the Burnside functor BK G. For instance, we find the first four top factors of the radical series of BK G for a p-group G, and assuming further that G is an abelian p-group we find the radical series of BK G. © 2009 Elsevier Inc. All rights reserved.