On torsion-free hypercentral groups with all subgroups subnormal. (English) Zbl 0675.20030
The author shows that a torsion free group which is hypercentral of length \(\omega\) in which all subgroups are subnormal is already nilpotent.
Reviewer: H.Heineken
MSC:
| 20F19 | Generalizations of solvable and nilpotent groups |
| 20E15 | Chains and lattices of subgroups, subnormal subgroups |
| 20E34 | General structure theorems for groups |
References:
| [1] | DOI: 10.1112/blms/15.3.229 · Zbl 0491.20025 · doi:10.1112/blms/15.3.229 |
| [2] | Segal, Poly cyclic groups 82 (1983) · doi:10.1017/CBO9780511565953 |
| [3] | Robinson, A course in the theory of groups 80 (1982) · Zbl 0483.20001 · doi:10.1007/978-1-4684-0128-8 |
| [4] | DOI: 10.1112/blms/18.4.343 · Zbl 0569.20028 · doi:10.1112/blms/18.4.343 |
| [5] | DOI: 10.1016/0021-8693(68)90086-0 · Zbl 0167.29001 · doi:10.1016/0021-8693(68)90086-0 |
| [6] | DOI: 10.1112/blms/15.3.235 · Zbl 0506.20012 · doi:10.1112/blms/15.3.235 |
| [7] | Robinson, Finiteness conditions and generalised soluble groups 2 (1972) |
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