The socle of a projective Mackey functor for a p-group
نویسندگان
چکیده
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A Mackey Functor Version of a Conjecture of Alperin
The notation np(G) differs from what appears in print elsewhere. In the notation of [5] and [10] one has np(G) = `(G)−f0(G) where `(G) is the number of simple kG-modules and f0(G) is the number of blocks of defect zero. In comparing different printed versions it may help to notice that for the stabilizer groups Gσ we have np(Gσ) = `(Gσ) because the Gσ always have a non-trivial normal p-subgroup...
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On the Projective Dimensions of Mackey Functors
We examine the projective dimensions of Mackey functors and cohomological Mackey functors. We show over a field of characteristic p that cohomological Mackey functors are Gorenstein if and only if Sylow p-subgroups are cyclic or dihedral, and they have finite global dimension if and only if the group order is invertible or Sylow subgroups are cyclic of order 2. By contrast, we show that the onl...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2009
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2008.12.024