Article
| 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 |
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| Category: | math |
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| 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 |
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| Date available: | 2022-11-28T11:35:46Z |
| Last updated: | 2023-04-11 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151127 |
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| 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 |
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