On $R$-conjugate-permutability of Sylow subgroups

Czechoslovak Mathematical Journal

Xianhe Zhao¹  Ruifang Chen² 

[1] (corresponding author),Ruifang Chen, Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, School of Mathematics and Information Sciences, Henan Normal University, No. 46, Jianshe East Road, Xinxiang, Henan, 453007, P. R. China,

关键词: $R$-conjugate-permutable subgroup;    nilpotent group;    quasinilpotent group;    Sylow subgroup;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

A subgroup $H$ of a finite group $G$ is said to be conjugate-permutable if $HH^g=H^gH$ for all $g\in G$. More generaly, if we limit the element $g$ to a subgroup $R$ of $G$, then we say that the subgroup $H$ is $R$-conjugate-permutable. By means of the $R$-conjugate-permutable subgroups, we investigate the relationship between the nilpotence of $G$ and the $R$-conjugate-permutability of the Sylow subgroups of $A$ and $B$ under the condition that $G=AB$, where $A$ and $B$ are subgroups of $G$. Some results known in the literature are improved and generalized in the paper.

【 授权许可】

Unknown