Document Type: Research Paper
Department of Mathematical Sciences, University of Bath, UK
Let $G$ be a powerful $p$-group. In this note we investigate when the Omega subgroups of the Agemo subgroups of $G$ are Powerfully Nilpotent. We discuss the difference between the cases when $p=2$ and when $p$ is an odd prime. Moreover this work gives an example of a characteristic subgroup of $G^p$ which is Powerfully Nilpotent but not strongly powerful.