# Paranormal subgroup

In symbols, ${\displaystyle H}$ is paranormal in ${\displaystyle G}$ if given any ${\displaystyle g}$ in ${\displaystyle G}$, the subgroup ${\displaystyle K}$ generated by ${\displaystyle H}$ and ${\displaystyle H^{g}}$ is also equal to ${\displaystyle H^{K}}$. Equivalently, a subgroup is paranormal if its weak closure and normal closure coincide in all intermediate subgroups.