On the nilpotency of some modules over group rings. (English. Ukrainian original) Zbl 1537.20011
Ukr. Math. J. 75, No. 10, 1573-1589 (2024); translation from Ukr. Mat. Zh. 75, No. 10, 1387-1401 (2023).
A group \(G\) is called perfect if \(G=[G, G]\). If \(G\) is solvable then \(G\) has no perfect sections.
The paper under review is devoted to the study of \(RG\)-modules that do not contain nonzero \(G\)-perfect factors. In particular, the authors show that if the group \(G\) is finite and \(R\) is a Dedekind domain with some additional restrictions, then these \(RG\)-modules are \(G\)-nilpotent.
The paper under review is devoted to the study of \(RG\)-modules that do not contain nonzero \(G\)-perfect factors. In particular, the authors show that if the group \(G\) is finite and \(R\) is a Dedekind domain with some additional restrictions, then these \(RG\)-modules are \(G\)-nilpotent.
Reviewer: Enrico Jabara (Venezia)
MSC:
| 20C05 | Group rings of finite groups and their modules (group-theoretic aspects) |
| 20C07 | Group rings of infinite groups and their modules (group-theoretic aspects) |
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