On finite groups with many supersoluble subgroups
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https://riunet.upv.es/handle/10251/151655
Cita bibliográfica
Ballester-Bolinches, A.; Esteban Romero, R.; Lu, J. (2017). On finite groups with many supersoluble subgroups. Archiv der Mathematik. 109(1):3-8. https://doi.org/10.1007/s00013-017-1041-4
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[EN] The solubility of a finite group with less than 6 non-supersoluble subgroups is confirmed in the paper. Moreover we prove that a finite insoluble group has exactly 6 non-supersoluble subgroups if and only if it is isomorphic to A5 or SL2 (5). Furthermore, it is shown that a finite insoluble group has exactly 22 non-nilpotent subgroups if and only if it is isomorphic to A5 or SL2 (5). This confirms a conjecture of Zarrin (Arch Math (Basel) 99:201 206, 2012).
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Archiv der Mathematik issn: 0003-889X