A note on the Green invariants in finite group modular representative theory. (Q927812)

Let \(\mathcal O\) be a complete Noetherian local commutative ring with algebraically closed residue field \(k\), and let \(N\) be a normal subgroup of a finite group \(G\). For an indecomposable \(\mathcal O[G/N]\)-module \(V\) and its inflation \(\widehat V\) to \(G\), the author relates the vertices, sources and Green correspondents of \(V\) and \(\widehat V\). Let \(W,X\) be \(\mathcal OG\)-modules such that \(W\otimes_{\mathcal O}X\) is indecomposable, and suppose that the restriction of \(W\) to a Sylow \(p\)-subgroup of \(G\) is a capped endo-permutation module. The author relates the vertices, sources and Green correspondents of \(X\) and \(W\otimes_{\mathcal O}X\). Reviewer's remark: The title of the paper should probably read ``A note on the Green invariants in finite group modular representation theory''.