Malnormal subgroup

In mathematics, in the field of group theory, a subgroup formula_1 of a group formula_2 is termed malnormal if for any formula_3 in formula_2 but not in formula_1, formula_1 and formula_7 intersect in the identity element.
Some facts about malnormality:
When "G" is finite, a malnormal subgroup "H" distinct from 1 and "G" is called a "Frobenius complement". The set "N" of elements of "G" which are, either equal to 1, or non-conjugate to any
element of "H", is a normal subgroup of "G", called the "Frobenius kernel", and "G" is the semi-direct product of "H" and "N" (Frobenius' theorem).