A focal subgroup theorem for outer commutator words

Details A focal subgroup theorem for outer commutator words A focal subgroup theorem for outer commutator words

2011-08-10

arxiv.org/abs/1108.2284v3

Mathematics

Group Theory

7 pages, 1 figure. To appear on Journal of Group Theory

Scientific paper

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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