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 ${\displaystyle AB=G}$, 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.^[1][2]

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

References

1. Su, Xiang Ying (1988), "Seminormal subgroups of finite groups", Journal of Mathematics 8 (1): 5–10, MR 963371.
2. Foguel, Tuval (1994), "On seminormal subgroups", Journal of Algebra 165 (3): 633–635, doi:10.1006/jabr.1994.1135, MR 1275925. Foguel writes: "Su introduces the concept of seminormal subgroups and using this tool he gives four sufficient conditions for supersolvability."