Abstract
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 pn, where p is an odd prime, the powerful nilpotency class of G is at most the integer part of . We also identify and explain what this means in terms of the powerful coclass of the group.
2010 Mathematics Subject Classification:
Declaration of interest
No potential conflict of interest was reported by the author(s).
Acknowledgments
The author is grateful to Gunnar Traustason and Gareth Tracey for their suggestions and advice with this article. The author is especially grateful for the suggestions of Gunnar Traustason with regard to the proof of Theorem 21.