Polynormal subgroup

In mathematics, in the field of group theory, a subgroup of a group is said to be polynormal if its closure under conjugation by any element of the group can also be achieved via closure by conjugation by some element in the subgroup generated.
In symbols, a subgroup formula_1 of a group formula_2 is called polynormal if for any formula_3 the subgroup formula_4 is the same as formula_5.
Here are the relationships with other subgroup properties: