Exterior square preserves divisibility for nilpotent groups
- Stem extension preserves divisibility for nilpotent groups
- Derived subgroup is divisibility-closed in nilpotent group
Proof using the Schur covering group
Recall that the exterior square can be defined as the derived subgroup of any Schur covering group of . The Schur covering group is itself nilpotent (of class at most one more than the class of ) and is a stem extension of . Facts (1) and (2) give the result.