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 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 semi-direct product of H and N (Frobenius' theorem).
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- Karrass, A.; Solitar, D. (1971), "The free product of two groups with a malnormal amalgamated subgroup", Canadian Journal of Mathematics, 23: 933–959, MR 0314992, doi:10.4153/cjm-1971-102-8.
- de la Harpe, Pierre; Weber, Claude (2011), Malnormal subgroups and Frobenius groups: basics and examples, arXiv:.
- Feit, Walter (1967), Characters of finite groups, W. A. Benjamin, Inc., New York-Amsterdam, pp. 133–139, MR 0219636.