Malnormal subgroup


In mathematics, in the field of group theory, a subgroup of a group is termed malnormal if for any in but not in, and 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.