On supersolubility in some groups with finitely generated Fitting radical

James C. Beidleman, Howard Smith
1992 Proceedings of the American Mathematical Society  
The groups G considered in this paper have the property that every normal nonsupersoluble subgroup of G has a finite, G-invariant, nonsupersoluble image. The structure of a certain radical, defined in terms of ascendant supersoluble subgroups, is determined. The main result is a supersolubility criterion for polycyclic groups.
doi:10.1090/s0002-9939-1992-1069288-6 fatcat:hpszei3fybhptd5mnl2e6ntqn4