Subgroup whose focal subgroup equals its derived subgroup
(Redirected from Subgroup whose focal subgroup equals its commutator 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]
Then, we require that:
i.e., the focal subgroup of equals its own commutator subgroup.
Relation with other properties
- Direct factor
- Central factor
- Central subgroup
- Conjugacy-closed normal subgroup
- Conjugacy-closed subgroup: For proof of the implication, refer Conjugacy-closed implies focal subgroup equals commutator subgroup and for proof of its strictness (i.e. the reverse implication being false) refer Focal subgroup equals commutator subgroup not implies conjugacy-closed.