On s-Quasinormal and c-Normal Subgroups of a Finite Group  

作　　者：Shi Rong LI 

机构地区：[1]Department of Mathematics, Guangxi University, Nanning, Guangxi 530004, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第4期647-654,共8页数学学报（英文版）

基　　金：the Natural Science Foundation of China;the Natural Science Foundation of Guangxi Autonomous Region (No.0249001)

摘　　要：Let F be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are shown： （1） G ∈ F if and only if there is a normal subgroup H such that G/H ∈ F and every maximal subgroup of all Sylow subgroups of H is either c-normal or s-quasinormally embedded in G; （2） G ∈F if and only if there is a soluble normal subgroup H such that G/H∈F and every maximal subgroup of all Sylow subgroups of F（H）, the Fitting subgroup of H, is either e-normally or s-quasinormally embedded in G.Let F be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are shown： （1） G ∈ F if and only if there is a normal subgroup H such that G/H ∈ F and every maximal subgroup of all Sylow subgroups of H is either c-normal or s-quasinormally embedded in G; （2） G ∈F if and only if there is a soluble normal subgroup H such that G/H∈F and every maximal subgroup of all Sylow subgroups of F（H）, the Fitting subgroup of H, is either e-normally or s-quasinormally embedded in G.

关 键 词：s-quasinormally embedded subgroup c-normal subgroup p-nilpotent group saturated formation 

分 类 号：O152[理学—数学]