| Title:
|
On weakly $s$-permutably embedded subgroups (English) |
| Author:
|
Li, Changwen |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
21-29 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Suppose $G$ is a finite group and $H$ is a subgroup of $G$. $H$ is said to be $s$-permutably embedded in $G$ if for each prime $p$ dividing $|H|$, a Sylow $p$-subgroup of $H$ is also a Sylow $p$-subgroup of some $s$-permutable subgroup of $G$; $H$ is called weakly $s$-permutably embedded in $G$ if there are a subnormal subgroup $T$ of $G$ and an $s$-permutably embedded subgroup $H_{se}$ of $G$ contained in $H$ such that $G=HT$ and $H\cap T\leq H_{se}$. We investigate the influence of weakly $s$-permutably embedded subgroups on the $p$-nilpotency and $p$-supersolvability of finite groups. (English) |
| Keyword:
|
weakly $s$-permutably embedded subgroups |
| Keyword:
|
$p$-nilpotent |
| Keyword:
|
$n$-maximal subgroup |
| MSC:
|
20D10 |
| MSC:
|
20D20 |
| idZBL:
|
Zbl 1222.20014 |
| idMR:
|
MR2828373 |
| . |
| Date available:
|
2011-03-08T17:34:17Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141425 |
| . |
| Reference:
|
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| . |
