Title: "A remark on the Dade group and the Burnside group"
Author: Serge Bouc

{Abstract: The object of this note is to show that the formula for
tensor induction of relative syzygies in the Dade group, stated in [1],
can be viewed as a special case of a functorial homomorphism from the
dual $B^*$ of the Burnside group to the subgroup $D^\Omega$ of the Dade
group generated by relative syzygies. It follows that there exists a
short exact sequence of functors
$$0\to R_\Q^*\to B^*\to D^{\Omega}/D^{\Omega}_{tors}\to 0$$
where $R_\Q$ is the functor of rational representations. This may be
viewed as an improvement (from $\Q$ to $\Z$) of Theorem~D of [2].

[1] S. Bouc. Tensor induction of relative syzygies. J. reine angew. Math. 523 (2000),113-171.
[2] S. Bouc and J. Thévenaz. The group of endo-permutation modules. Invent. Math. 139 (2000), 275-349.
}