# Omegas of agemos in powerful groups

Document Type: Research Paper

Author

Department of Mathematical Sciences, University of Bath, UK

Abstract

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.

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