Normal Subgroups of Powerful $p$ -groups

James Williams

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arXiv · 1908.07030

Normal Subgroups of Powerful $p$ -groups

James Williams

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Abstract

In this note we show that if $p$ is an odd prime and $G$ is a powerful $p$-group with $N\leq G^{p}$ and $N$ normal in $G$, then $N$ is powerfully nilpotent. An analogous result is proved for $p=2$ when $N\leq G^{4}$.

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BibTeX RIS

James Williams. 2019-08-19. Normal Subgroups of Powerful $p$ -groups. https://arxiv.org/abs/1908.07030

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