Malnormal subgroup

Malnormal subgroup: In mathematics, in the field of group theory, a subgroup $H$ of a group $G$ is termed malnormal if for any $x$ in $G$ but not in $H$ , $H$ and $H x$ intersect in the identity element.

Some facts about malnormality:

An 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 TI subgroup.

Categories:
Subgroup properties

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