IA-automorphism group of finite p-group is p-group
- IA-automorphism group of finite nilpotent group has precisely the same prime factors of order as the derived subgroup
- Prime power order implies nilpotent
- IA-automorphism group of nilpotent group equals stability group of lower central series
- Stability group of subnormal series of finite p-group is p-group
The proof follows directly by combining Facts (1), (2), and (3).