Seminormal subgroup

In mathematics, in the field of group theory, a subgroup formula_1 of a group formula_2 is termed seminormal if there is a subgroup formula_3 such that formula_4, and for any proper subgroup formula_5 of formula_3, formula_7 is a proper subgroup of formula_2.
This definition of seminormal subgroups is due to Xiang Ying Su.
Every normal subgroup is seminormal. For finite groups, every quasinormal subgroup is seminormal.