| 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:
|
http://hdl.handle.net/10338.dmlcz/144885 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| . |
