On defect groups of the Mackey algebras for finite groups (Q1365123)

Let \(G\) be a finite group and \(R\) a commutative ring. The Mackey algebra \(\mu_R(G)\) was used by J. Thévenaz and P. Webb in connection with their work on Mackey functors. It appeared in earlier work by T. Yoshida under the name ``span ring''. When \(R\) is a field of characteristic \(p\) then the blocks of \(\mu_R(G)\) can be parametrized by conjugacy classes of pairs \((J,B)\) consisting of a \(p\)-perfect subgroup \(J\) of \(G\) and a block \(B\) of the group algebra \(R[N_G(J)/J]\). The author defines the defect groups of a block of \(\mu_R(G)\) in terms of a certain Green functor. For a block \(B\) of \(RG\), the defect groups of \(B\) are shown to be contained in defect groups of the block of \(\mu_R(G)\) parametrized by \((1,B)\).