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- Title
On finite groups with many supersoluble subgroups.
- Authors
Ballester-Bolinches, A.; Esteban-Romero, R.; Lu, Jiakuan
- Abstract
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 $$A_5$$ or $${{\mathrm{SL}}}_2(5)$$ . Furthermore, it is shown that a finite insoluble group has exactly 22 non-nilpotent subgroups if and only if it is isomorphic to $$A_5$$ or $${{\mathrm{SL}}}_2(5)$$ . This confirms a conjecture of Zarrin (Arch Math (Basel) 99:201-206, 2012).
- Publication
Archiv der Mathematik, 2017, Vol 109, Issue 1, p3
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s00013-017-1041-4