Note on the axioms of Bouc (Q1184189)

\textit{S. Bouc} [J. Algebra 139, 395-445 (1991; Zbl 0735.19001)] had studied maps \(P\mapsto M(P)\) associating to any module \(M\) over a subgroup \(H\) of \(G\) and any \(p\)-subgroup \(P\) of \(H\) a module \(M(P)\) for \(N_ H(P)\) and satisfying a list of seven axioms. He had used such maps to obtain pairwise orthogonal projectors on the Green ring. In the present paper the author shows how both Bouc's axioms and the proofs of his results can be simplified by using the decomposition of the Green ring into residual Green rings obtained in the author's earlier paper [J. Algebra 116, 7-129 (1988; Zbl 0658.20004)].