Paranormal subgroup

In mathematics, in the field of group theory, a paranormal subgroup is a subgroup such that the subgroup generated by it and any conjugate of it, is also generated by it and a conjugate of it within that subgroup.

Equivalently, a subgroup is paranormal if its weak closure and normal closure coincide in all intermediate subgroups.

Here are some facts relating paranormality to other subgroup properties: Kantor, William M.; Martino, Lino Di (12 January 1995).

Groups of Lie Type and Their Geometries.

Cambridge University Press.