6533b820fe1ef96bd12792f1

RESEARCH PRODUCT

On finite groups with many supersoluble subgroups

Ramon Esteban-romeroRamon Esteban-romeroAdolfo Ballester-bolinchesJiakuan Lu

subject

0301 basic medicineFinite groupConjectureSoluble groupGroup (mathematics)General Mathematics010102 general mathematicsGrups Teoria de01 natural sciencesCombinatoricsMathematics::Group Theory03 medical and health sciences030104 developmental biologyLocally finite groupSupersoluble subgroup0101 mathematicsFinite groupMathematics::Representation TheoryMATEMATICA APLICADAMatemàticaMathematics

description

[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).

yearjournalcountryeditionlanguage
2017-04-08
10.1007/s00013-017-1041-4https://doi.org/10.1007/s00013-017-1041-4