Malnormal subgroup
Encyclopedia : M : MA : MAL : 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.
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