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:
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[2] | Segal, Poly cyclic groups 82 (1983) · doi:10.1017/CBO9780511565953 |
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[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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