On supersolubility in some groups with finitely generated Fitting radical

Beidleman, James C.; Smith, Howard

doi:10.1090/S0002-9939-1992-1069288-6

On supersolubility in some groups with finitely generated Fitting radical
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by James C. Beidleman and Howard Smith

Proc. Amer. Math. Soc. 114 (1992), 319-324

DOI: https://doi.org/10.1090/S0002-9939-1992-1069288-6

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Abstract:

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.

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