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On supersolubility in some groups with finitely generated Fitting radical


Authors: James C. Beidleman and Howard Smith
Journal: Proc. Amer. Math. Soc. 114 (1992), 319-324
MSC: Primary 20F16
DOI: https://doi.org/10.1090/S0002-9939-1992-1069288-6
MathSciNet review: 1069288
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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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DOI: https://doi.org/10.1090/S0002-9939-1992-1069288-6
Article copyright: © Copyright 1992 American Mathematical Society