A remark on the Dade group and the Burnside group

The object of this note is to show that the formula for tensor induction of relative syzygies in the Dade group, stated in [S. Bouc, J. Reme Angew. Math. 523 (2000) 113], 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 --> R-Q* --> B* --> D-Omega/D-tors(Omega) --> 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 [Invent. Math. 139 (2000) 275]. (C) 2003 Elsevier Inc. All rights reserved.