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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.

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 0963371.
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."

• Subgroup properties