Geodesic
On torsion-free hypercentral groups with all subgroups subnormal
Glasgow mathematical journal, Tome 31 (1989) no. 2, pp. 193-194

Voir la notice de l'article provenant de la source Cambridge University Press

There is no example known of a non-nilpotent, torsion-free group which has all of its subgroups subnormal. It was proved in [3] that a torsion-free solvable group with all of its proper subgroups subnormal and nilpotent is itself nilpotent, but that seems to be the only published result in this area which is concerned specifically with torsion-free groups. Possibly the extra hypothesis that the group be hypercentral is sufficient to ensure nilpotency, though this is certainly not the case for groups with torsion, as was shown in [7]. The groups exhibited in that paper were seen to have hypercentral length ω + 1, and we know from [8] that further restricting the hypercentral length can lead to some positive results. Here we shall prove the following theorem. 
Smith, Howard. On torsion-free hypercentral groups with all subgroups subnormal. Glasgow mathematical journal, Tome 31 (1989) no. 2, pp. 193-194. doi: 10.1017/S0017089500007734
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