Geodesic
The Wielandt subgroup of a polycyclic group
Glasgow mathematical journal, Tome 33 (1991) no. 2, pp. 231-234

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

The purpose of this paper is to establish some basic properties of the Wielandt subgroup of a polycyclic group. The Wielandt subgroup of a group G is defined to be the intersection of the normalisers of all the subnormal subgroups of G and is denoted by ω(G). In 1958 Wielandt [9] showed that any minimal normal subgroup with the minimum condition on subnormal subgroups is contained in the Wielandt subgroup: it follows that the Wielandt subgroup of an artinian group is nontrivial. In contrast, the Wielandt subgroup of a polycyclic group can be trivial; an easy example is given by the infinite dihedral group. We will show that the Wielandt subgroup of a polycyclic group is close to being central. 
Cossey, John. The Wielandt subgroup of a polycyclic group. Glasgow mathematical journal, Tome 33 (1991) no. 2, pp. 231-234. doi: 10.1017/S0017089500008260
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