Conjugation-invariantly permutably complemented subgroup
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
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- It is permutably complemented, viz the set of its permutable complements is empty
- The set of its permutable complements is closed under conjugation. In other words, any conjugate of a permutable complement is also a permutable complement.
Definition with symbols
- There exists a subgroup of such that and is trivial (in other words, a permutable complement of in )
- If and are permutable complements, then and are also permutable complements for any .