Groups in which every infinite subnormal subgroup is normal
In his study of T-groups (i.e. groups in which every subnormal subgroup is normal), \textit{D. J. S. Robinson} [Proc. Camb. Philos. Soc. 60, 21-38 (1964; Zbl 0123.24901)] showed that a soluble T-group is metabelian. The authors define an IT-group to be a group in which every infinite subnormal subgroup is normal and study soluble IT-groups. In particular, it is shown that if G is an infinite soluble IT-group then G'' is cyclic of prime power order so that G has derived length \(\leq 3\). More detailed results are given showing how to construct all infinite soluble IT-groups which are not T-groups.
scientific article; zbMATH DE number 3912609