| Title:
|
Finite $p$-nilpotent groups with some subgroups weakly $\mathcal {M}$-supplemented (English) |
| Author:
|
Dong, Liushuan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
291-297 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Suppose that $G$ is a finite group and $H$ is a subgroup of $G$. Subgroup $H$ is said to be weakly $\mathcal {M}$-supplemented in $G$ if there exists a subgroup $B$ of $G$ such that (1) $G=HB$, and (2) if $H_{1}/H_{G}$ is a maximal subgroup of $H/H_{G}$, then $H_{1}B=BH_{1}<G$, where $H_{G}$ is the largest normal subgroup of $G$ contained in $H$. We fix in every noncyclic Sylow subgroup $P$ of $G$ a subgroup $D$ satisfying $1<|D|<|P|$ and study the $p$-nilpotency of $G$ under the assumption that every subgroup $H$ of $P$ with $|H|=|D|$ is weakly $\mathcal {M}$-supplemented in $G$. Some recent results are generalized. (English) |
| Keyword:
|
$p$-nilpotent group |
| Keyword:
|
weakly $\mathcal {M}$-supplemented subgroup |
| Keyword:
|
finite group |
| MSC:
|
20D10 |
| MSC:
|
20D20 |
| idZBL:
|
07217135 |
| idMR:
|
MR4078360 |
| DOI:
|
10.21136/CMJ.2019.0273-18 |
| . |
| Date available:
|
2020-03-10T10:20:45Z |
| Last updated:
|
2022-04-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148056 |
| . |
| 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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| . |
