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arXiv · 1108.2284

A focal subgroup theorem for outer commutator words

Cristina Acciarri·Gustavo A. Fernández-Alcober·Pavel Shumyatsky
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Abstract

Let $G$ be a finite group of order $p^am$, where $p$ is a prime and $m$ is not divisible by $p$, and let $P$ be a Sylow $p$-subgroup of $G$. If $w$ is an outer commutator word, we prove that $P\cap w(G)$ is generated by the intersection of $P$ with the set of $m$th powers of all values of $w$ in $G$

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Cristina Acciarri, Gustavo A. Fernández-Alcober, Pavel Shumyatsky. 2011-08-10. A focal subgroup theorem for outer commutator words. https://arxiv.org/abs/1108.2284

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