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
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the projective cover of a simple Mackey
functor for
G of the form
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we next try to answer the question: how are the Mackey
functors
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and
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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
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, 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
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is the projective cover of the simple
![]()
-module
V where the coefficient ring
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is a field, we finally study evaluations of Mackey
functors.