| Title:
|
A note on weakly-supplemented subgroups and the solvability of finite groups (English) |
| Author:
|
Liang, Xin |
| Author:
|
Xu, Baiyan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
72 |
| Issue:
|
4 |
| Year:
|
2022 |
| Pages:
|
1045-1046 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Suppose that $G$ is a finite group and $H$ is a subgroup of $G$. The subgroup $H$ is said to be weakly-supplemented in $G$ if there exists a proper subgroup $K$ of $G$ such that $G=HK$. In this note, by using the weakly-supplemented subgroups, we point out several mistakes in the proof of Theorem 1.2 of Q. Zhou (2019) and give a counterexample. (English) |
| Keyword:
|
weakly-supplemented subgroup |
| Keyword:
|
solvable group |
| Keyword:
|
finite group |
| MSC:
|
20D10 |
| MSC:
|
20D20 |
| idZBL:
|
Zbl 07655780 |
| idMR:
|
MR4517593 |
| DOI:
|
10.21136/CMJ.2022.0326-21 |
| . |
| Date available:
|
2022-11-28T11:35:46Z |
| Last updated:
|
2025-01-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151127 |
| . |
| Reference:
|
[1] Hall, P.: A characteristic property of soluble groups.J. Lond. Math. Soc. 12 (1937), 198-200. Zbl 0016.39204, MR 1575073, 10.1112/jlms/s1-12.2.198 |
| Reference:
|
[2] Huppert, B.: Endliche Gruppen. I.Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen 134. Springer, Berlin (1967), German. Zbl 0217.07201, MR 0224703, 10.1007/978-3-642-64981-3 |
| Reference:
|
[3] Zhou, Q.: On weakly-supplemented subgroups and the solvability of finite groups.Czech. Math. J. 69 (2019), 331-335. Zbl 07088787, MR 3959947, 10.21136/CMJ.2018.0301-17 |
| . |
