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:10.2307/2159649 fatcat:elzr6os3oneqfpqhsmpb4umepm