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A note on weakly-supplemented subgroups and the solvability of finite groups
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 1045-1046
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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.
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.
DOI : 10.21136/CMJ.2022.0326-21
Classification : 20D10, 20D20
Keywords: weakly-supplemented subgroup; solvable group; finite group 
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Liang, Xin; Xu, Baiyan. A note on weakly-supplemented subgroups and the solvability of finite groups. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 1045-1046. doi: 10.21136/CMJ.2022.0326-21

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[2] Huppert, B.: Endliche Gruppen. I. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen 134. Springer, Berlin (1967), German. | DOI | MR | JFM

[3] Zhou, Q.: On weakly-supplemented subgroups and the solvability of finite groups. Czech. Math. J. 69 (2019), 331-335. | DOI | MR | JFM

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