Groups in which every finite subnormal subgroup is normal

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.