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- W4249922070 abstract "Publisher SummaryThis chapter investigates the p-permutation modules. The chapter provides various characterizations of p-permutation modules. In particular, it is shown that an indecomposable RG-module is a p-permutation module if and only if it has a trivial source. It is then demonstrated that any p-permutation FG-module lifts uniquely to a p-permutation RG-module, and show that the corresponding residue class map is surjective. The further characterizations of p-permutation modules via the notions of monomial and virtually monomial modules are presented. Important tool for the study of p-permutation modules is presented, namely the Brauer morphism. The corresponding theory is then applied for the study of Scott modules. A detailed investigation of vertices of p-permutation modules is presented. One of these properties asserts that, for any p-subgroup P of G, the number of nonisomorphic indecomposable p-permutation RG-modules with vertex P is equal to the number of F-conjugacy classes of p-regular elements of NG(P)/P. The prove of an interesting result is presented, which asserts that the NG(P)-algebras (EndF(V))(P) and EndF(V(P)) are identifiable." @default.
- W4249922070 created "2022-05-12" @default.
- W4249922070 date "1995-01-01" @default.
- W4249922070 modified "2023-09-27" @default.
- W4249922070 title "Chapter 14: p-Permutation Modules" @default.
- W4249922070 doi "https://doi.org/10.1016/s0304-0208(09)70113-6" @default.
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