  The Brauer relations of a finite group $G$ are virtual differences of
non-isomorphic $G$-sets $X-Y$ which induce isomorphic permutation
$G$-representations $\mathbb Q[X]\simeq\mathbb Q[Y]$ over the rationals. These
relations have been classified by Tornehave-Bouc and Bartel-Dokchitser.
Motivated by stable homotopy theory, a relative version of Brauer relations for
$(G,C_p)$-bisets which are $C_p$-free have been classified by Kahn in case $G$
is an elementary Abelian $p$-group. In this paper we extend Kahn's
classification to the case when $G$ is a finite Abelian $p$-group.
