Paranormal implies weakly closed in intermediate nilpotent
Statement with symbols
Suppose are groups such that:
Then, is a Weakly closed subgroup (?) of .
For these definitions, denotes the conjugate subgroup by . (This is the right-action convention; however, adopting a left-action convention does not alter any of the proof details).
Further information: Paranormal subgroup
Weakly closed subgroup
Further information: Weakly closed subgroup
Suppose are groups. We say is weakly closed in with respect to if, for any such that , we have .
The proof follows directly from facts (1) and (2).