Seminormal subgroup

In mathematics, in the field of group theory, a subgroup ${\displaystyle A}$ of a group ${\displaystyle G}$ is termed seminormal if there is a subgroup ${\displaystyle B}$ such that ${\displaystyle AB=G}$, and for any proper subgroup ${\displaystyle C}$ of ${\displaystyle B}$, ${\displaystyle AC}$ is a proper subgroup of ${\displaystyle G}$.

This definition of seminormal subgroups is due to Xiang Ying Su.^[1][2]

Every normal subgroup is seminormal. For finite groups, every quasinormal subgroup is seminormal.