Powerfully Nilpotent Groups of Class 2

In this article, we investigate the powerful nilpotency class of powerfully nilpotent groups of standard nilpotency class 2. We outline the process of collecting data using the computer algebra system GAP, formulating a conjecture based on the data, and finally we prove the conjecture. In particular, we prove that for a powerfully nilpotent group of nilpotency class 2 and order p(n), where p is an odd prime, the powerful nilpotency class of G is at most the integer part of n/2 . We also identify and explain what this means in terms of the powerful coclass of the group.