Conjugacy-closed implies focal subgroup equals derived subgroup

From Groupprops
Jump to: navigation, search
DIRECT: The fact or result stated in this article has a trivial/direct/straightforward proof provided we use the correct definitions of the terms involved
View other results with direct proofs
VIEW FACTS USING THIS: directly | directly or indirectly, upto two steps | directly or indirectly, upto three steps|
VIEW: Survey articles about this
This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., conjugacy-closed subgroup) must also satisfy the second subgroup property (i.e., subgroup whose focal subgroup equals its commutator subgroup)
View all subgroup property implications | View all subgroup property non-implications
Get more facts about conjugacy-closed subgroup|Get more facts about subgroup whose focal subgroup equals its commutator subgroup

Statement

Suppose H is a conjugacy-closed subgroup of a group G. In other words, any two elements of H that are conjugate in G are in fact conjugate in H. Then, the focal subgroup of H equals its Commutator subgroup (?).

Related facts