# Seminormal subgroup

{{ safesubst:#invoke:Unsubst||\$N=Unreferenced |date=__DATE__ |\$B= {{#invoke:Message box|ambox}} }} 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.Template:Fact

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

A good reference for subgroup properties is "A Course in the Theory of Groups" by Derek J.S. Robinson.