Group Theory (CVIII)
Another Counting Principle
Using the theorem ' If O(G) = p^n , where p is a prime number, then Z(G) ≠ (e) ' as a tool, prove that
if O(G) = p^n where p is a prime number, then G has a subgroup of order p^α for all 0 < α ≤ n .
This is a group theory proof regarding permutations and counting.