| Title:
|
On solvability of finite groups with some $ss$-supplemented subgroups (English) |
| Author:
|
Lu, Jiakuan |
| Author:
|
Qiu, Yanyan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
427-433 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A subgroup $H$ of a finite group $G$ is said to be $ss$-supplemented in $G$ if there exists a subgroup $K$ of $G$ such that $G=HK$ and $H\cap K$ is $s$-permutable in $K$. In this paper, we first give an example to show that the conjecture in A. A. Heliel's paper (2014) has negative solutions. Next, we prove that a finite group $G$ is solvable if every subgroup of odd prime order of $G$ is $ss$-supplemented in $G$, and that $G$ is solvable if and only if every Sylow subgroup of odd order of $G$ is $ss$-supplemented in $G$. These results improve and extend recent and classical results in the literature. (English) |
| Keyword:
|
$ss$-supplemented subgroup |
| Keyword:
|
solvable group |
| Keyword:
|
supersolvable group |
| MSC:
|
20D10 |
| MSC:
|
20D20 |
| MSC:
|
20D40 |
| idZBL:
|
Zbl 06486957 |
| idMR:
|
MR3360437 |
| DOI:
|
10.1007/s10587-015-0186-1 |
| . |
| Date available:
|
2015-06-16T17:51:39Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144280 |
| . |
| Reference:
|
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| Reference:
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