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

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Ballester-Bolinches, Adolfo Perfil; Esteban Romero, Ramón Perfil; Qiao, ShouHong
This document is a artículoDate2016

Este documento está disponible también en : http://hdl.handle.net/10550/68727
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.

    Ballester-Bolinches, Adolfo Esteban Romero, Ramón Qiao, ShouHong 2016 A note on a result of Guo and Isaacs about p-supersolubility of finite groups Archiv der Mathematik 106 6 501 506
https://doi.org/10.1007/s00013-016-0901-7

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