Abstract
A group G is called a T-group if normality in G is a transitive relation, i.e. all subnormal subgroups of G are normal. The structure of soluble T-groups is well-known, and several authors have investigated groups in which the normality condition is imposed only to a relevant system of subnormal subgroups. We consider here (generalized) soluble groups in which all finite subnormal subgroups are normal.
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