Class-preserving automorphism group of finite p-group is p-group
Suppose is a finite -group, i.e., a Group of prime power order (?) where the prime is . Let denote the group of Class-preserving automorphism (?)s of , i.e., the automorphisms that send every element to within its conjugacy class. Then, is also a -group.
- Class-preserving implies stability automorphism of central series
- Stability group of subnormal series of p-group is p-group
The proof follows directly from facts (1) and (2).