Seminormal subgroup

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

This definition of seminormal subgroups is due to Xiang Ying Su.

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