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Title: On $R$-conjugate-permutability of Sylow subgroups (English)
Author: Zhao, Xianhe
Author: Chen, Ruifang
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 66
Issue: 1
Year: 2016
Pages: 111-117
Summary lang: English
Category: math
Summary: A subgroup $H$ of a finite group $G$ is said to be conjugate-permutable if $HH^{g}=H^{g}H$ 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. (English)
Keyword: $R$-conjugate-permutable subgroup
Keyword: nilpotent group
Keyword: quasinilpotent group
Keyword: Sylow subgroup
MSC: 20D10
MSC: 20D20
idZBL: Zbl 06587877
idMR: MR3483226
DOI: 10.1007/s10587-016-0243-4
Date available: 2016-04-07T14:59:17Z
Last updated: 2020-07-03
Stable URL:
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