On groups satisfying the maximal and the minimal conditions for subnormal subgroups of infinite order or index. (English) Zbl 1197.20021
Summary: We prove that a generalized radical group satisfying the maximal condition for subnormal subgroups of infinite order (the minimal condition for subnormal subgroups of infinite index, respectively) is soluble-by-finite. Such result generalizes that obtained by D. H. Paek [in Commun. Algebra 29, No. 7, 3069-3081 (2001; Zbl 0984.20017)].
MSC:
| 20E15 | Chains and lattices of subgroups, subnormal subgroups |
| 20F19 | Generalizations of solvable and nilpotent groups |
| 20F22 | Other classes of groups defined by subgroup chains |
