Czechoslovak Mathematical Journal, Vol. 72, No. 4, pp. 1045-1046, 2022
A note on weakly-supplemented subgroups and the solvability of finite groups
Xin Liang, Baiyan Xu
Received September 6, 2021. Published online March 18, 2022.
Abstract: 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.
Keywords: weakly-supplemented subgroup; solvable group; finite group