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The solubility of a finite group with less than [Formula: see text] supersoluble subgroups is confirmed in this paper. Moreover, we prove that a finite insoluble group has exactly [Formula:… Click to show full abstract
The solubility of a finite group with less than [Formula: see text] supersoluble subgroups is confirmed in this paper. Moreover, we prove that a finite insoluble group has exactly [Formula: see text] supersoluble subgroups if and only if it is isomorphic to [Formula: see text]. Furthermore, it is shown that a finite group with less than [Formula: see text] conjugacy classes of supersoluble subgroups is soluble, and the only finite insoluble group with [Formula: see text] conjugacy classes of supersoluble subgroups is isomorphic to [Formula: see text].
Journal Title: Journal of Algebra and Its Applications
Year Published: 2019
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