RESTRICTING GLOBALLY-DEFINED MACKEY FUNCTORS TO NILPOTENT FINITE GROUPS

Abstract

Let B be the Burnside ring considered as a globally-defined Mackey functor, and k be a field of positive characteristic q. We prove that, when k ⊗ℤ B is restricted to nilpotent groups of order prime to q, the only simple Mackey functors that can appear as subquotients of it are of the form SE,k, where E is the direct product of elementary abelian p-groups. In the special case k = 𝔽2, the simple Mackey functor SE,𝔽2 must appear as a filtration factor in 𝔽2 ⊗ℤ B for every direct product of elementary abelian p-groups E of odd order.