Malnormal subgroup

In group theory, a subgroup H of a group G is termed malnormal if for any group element x not in H , H and xHx^{-1} 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 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 semidirect product of H and N .

In group theory, a subgroup H of a group G is termed malnormal if for any group element x not in H , H and xHx^{-1} 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 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 semidirect product of H and N .

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