Recovering a cohomological Mackey Functor from its restriction to Sylow subgroups

We explain how to recover the top level of a cohomological G-Mackey functor $\underline{M}$ from the restriction of $\underline{M}$ to each of the Sylow subgroups of G. As an application, we compute the Mackey functor valued G-equivariant homology groups of a point with constant $\mathbb{Z}$-coefficients when G has order pq for odd primes p<q. We also indicate how the calculation goes for $G=A_4$.

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