Bulletin of the
Korean Mathematical Society BKMS

A finite group $G$ is called a $\mathcal{QNS}$-group if every minimal subgroup $X$of $G$ is either quasinormal in $G$ or self-normalizing. In this paper the authors classify the non-$\mathcal{QNS}$-groups whose proper subgroups are all $\mathcal{QNS}$-groups.

Keywords: minimal subgroups, quasinormal subgroups, self-normalizing subgroups, $\mathcal{QNS}$-groups, minimal non-$\mathcal{QNS}$-groups

MSC numbers: 20D35, 20E34