Groups whose non-subnormal subgroups have a transitive normality relation.
The authors consider groups whose non-subnormal subgroups are T-groups and whose subnormal subgroups are of bounded defect or of unrestricted defect. They call a group \(G\) \(k\)-metahamiltonian if every nonabelian subgroup of \(G\) is subnormal with defect at most \(k\). In the case that there is no restriction to the defect examples of results are the following: If \(G\) is nontrivial and locally finite, then \(G\) contains a nontrivial normal Sylow subgroup (Theorem 2.8), if \(G\) is finitely generated and soluble, then \(G\) is nilpotent or Abelian-by-finite (Lemma 2.9), if \(G\) is hyper-(locally (soluble-by-finite)), then \(G\) is soluble and locally nilpotent or of derived length 4 (Theorem 2.10). If the defect is bounded by \(k\), we have if \(G\) is locally soluble, it is \(k\)-metahamiltonian (Theorem 3.5).
scientific article; zbMATH DE number 2016641