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We give a conjectural description for the kernel of the map assigning to eachfinite $\mathbb Z_p$-free $G\times\mathbb Z_p$-set its rational permutationmodule where G is a finite p-group. We prove that this conjecture is true whenG is an elementary abelian p-group or a cyclic p-group.

The Relative Burnside Kernel - The Elementary Abelian Case