6533b7defe1ef96bd1275df9
RESEARCH PRODUCT
A note on a result of Guo and Isaacs about p-supersolubility of finite groups
Adolfo Ballester-bolinchesShouhong QiaoRamon Esteban-romeroRamon Esteban-romerosubject
Discrete mathematicsFinite groupCoprime integersP-supersoluble groupGeneral MathematicsS-semipermutable subgroup010102 general mathematicsSylow theoremsGrups Teoria deOrder (ring theory)01 natural sciencesPrime (order theory)CombinatoricsGlobal informationLocally finite group0103 physical sciences010307 mathematical physicsFinite group0101 mathematicsMATEMATICA APLICADAMatemàticaMathematicsdescription
In this note, global information about a finite group is obtained by assuming that certain subgroups of some given order are S-semipermutable. Recall that a subgroup H of a finite group G is said to be S-semipermutable if H permutes with all Sylow subgroups of G of order coprime to . We prove that for a fixed prime p, a given Sylow p-subgroup P of a finite group G, and a power d of p dividing such that , if is S-semipermutable in for all normal subgroups H of P with , then either G is p-supersoluble or else . This extends the main result of Guo and Isaacs in (Arch. Math. 105:215-222 2015). We derive some theorems that extend some known results concerning S-semipermutable subgroups.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-01-01 | Archiv der Mathematik |