In group theory, a subgroup of a group is termed malnormal if for any group element not in , and intersect only in the identity element.
Some facts about malnormality:
The intersection of malnormal subgroups is malnormal.
Malnormality is transitive; that is, a malnormal subgroup of a malnormal subgroup is malnormal.
The trivial subgroup and the whole group are malnormal subgroups. A normal subgroup that is also malnormal must be one of these.
Every malnormal subgroup is a special type of C-group called a trivial intersection subgroup, or TI subgroup.
When is finite, a malnormal subgroup distinct from 1 and is called a "Frobenius complement". The set of elements of which are either equal to 1 or non-conjugate to any element of is a normal subgroup of , called the "Frobenius kernel", and is the semidirect product of and .
Notes
References