Endo-monomial modules over \(p\)-groups and their classification in the Abelian case.
The author defines and investigates endo-monomial \({\mathcal O}P\)-modules, for a finite \(p\)-group \(P\) and a suitable \(p\)-adic ring \(\mathcal O\), where \(p\) is a prime number. An \({\mathcal O}P\)-module \(M\) which is finitely generated and free over \(\mathcal O\) is called endo-monomial if its \(\mathcal O\)-endomorphism ring \(\text{End}_{\mathcal O}(M)\) is a monomial \({\mathcal O}P\)-module. The author shows that large parts of \textit{E. C. Dade}'s theory of endo-permutation modules [Ann. Math. (2) 107, 459-494 (1978; Zbl 0395.16007), ibid. 108, 317-346 (1978; Zbl 0404.16003)] carry over to endo-monomial modules. The main result of the paper shows that, when \(P\) is Abelian, every indecomposable endo-monomial \({\mathcal O}P\)-module with vertex \(P\) is already an endo-permutation module.
scientific article; zbMATH DE number 2105362
scientific article