Search results for "P-supersoluble"
showing 3 items of 3 documents
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.
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.
Z-permutable subgroups of finite groups
2016
Let Z be a complete set of Sylow subgroups of a finite group G, that is, a set composed of a Sylow p-subgroup of G for each p dividing the order of G. A subgroup H of G is called Z-permutable if H permutes with all members of Z. The main goal of this paper is to study the embedding of the Z-permutable subgroups and the influence of Z-permutability on the group structure.