| Title:
|
The influence of weakly-supplemented subgroups on the structure of finite groups (English) |
| Author:
|
Kong, Qingjun |
| Author:
|
Liu, Qingfeng |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
173-182 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A subgroup $H$ of a finite group $G$ is weakly-supplemented in $G$ if there exists a proper subgroup $K$ of $G$ such that $G=HK$. In the paper it is proved that a finite group $G$ is $p$-nilpotent provided $p$ is the smallest prime number dividing the order of $G$ and every minimal subgroup of $P\cap G'$ is weakly-supplemented in $N_{G}(P),$ where $P$ is a Sylow $p$-subgroup of $G$. As applications, some interesting results with weakly-supplemented minimal subgroups of $P\cap G'$ are obtained. (English) |
| Keyword:
|
weakly-supplemented subgroup |
| Keyword:
|
$p$-nilpotent group |
| Keyword:
|
supersolvable group |
| MSC:
|
20D10 |
| MSC:
|
20D20 |
| idZBL:
|
Zbl 06391485 |
| idMR:
|
MR3247453 |
| DOI:
|
10.1007/s10587-014-0092-y |
| . |
| Date available:
|
2014-09-29T09:50:22Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143958 |
| . |
| 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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| . |
