On a class of modules that are close to Noetherian.
Let \(RG\) be the group ring of a group \(G\) over a commutative Noetherian ring \(R\) and let \(A\) be an \(RG\)-module. In this paper the author finds sufficient conditions for \(A\) and \(G\) such that a locally soluble group \(G\) is soluble. For example, let \(G\) be a locally soluble group either of infinite Abelian section rank, or of infinite special rank. If the quotient \(R\)-module \(A/C_A(H)\) is Noetherian for every proper subgroup \(H\) of \(G\) such that \(H\) is, respectively, of infinite Abelian section rank or of infinite special rank, then \(G\) is soluble. Moreover, suppose that \(G\) is a locally soluble group with infinite \(p\)-rank \(r_p(G)\) for some prime number \(p\). If \(A/C_A(H)\) is Noetherian for every proper subgroup \(H\) with infinite \(p\)-rank \(r_p(H)\), then \(G\) is soluble.
scientific article; zbMATH DE number 5915294