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

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

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Ballester-Bolinches, Adolfo; Esteban Romero, Ramón; Qiao, ShouHong

This document is a artículoDate2016

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 |H|. 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 |G| such that 1≤d<|P| , if H∩Op(G) is S-semipermutable in Op(G) for all normal subgroups H of P with |H|=d , then either G is p-supersoluble or else |P∩Op(G)|>d . 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.

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