Search results for "P-supersoluble group"

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A note on a result of Guo and Isaacs about p-supersolubility of finite groups

2016

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.

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 APLICADAMatemàticaMathematicsArchiv der Mathematik
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On the supersoluble hypercentre of a finite group

2016

[EN] We give some sufficient conditions for a normal p-subgroup P of a finite group G to have every G-chief factor below it cyclic. The S-permutability of some p-subgroups of O^p(G)plays an important role. Some known results can be reproved and some others appear as corollaries of our main theorems.

Discrete mathematicsFinite groupP-supersoluble groupGeneral MathematicsS-semipermutable subgroup010102 general mathematicsGrups Teoria de01 natural sciencesMathematics::Group Theory0103 physical sciences010307 mathematical physicsFinite group0101 mathematicsMATEMATICA APLICADAMatemàticaMathematicsMonatshefte für Mathematik
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