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18.106 (2014)

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Let $R$ be a group that acts coprimely on the finite group $G$. Let $p$ be a prime, let $P$ be the unique maximal $R C_G(R)$-invariant $p$-subgroup of $G$ and assume that $C_G(O_p(G)) \leqslant O_p(G)$. If $p > 3$ then $P$ contains a nontrivial characteristic subgroup that is normal in $G$ (P. Flavell, J. Algebra, 257 (2002), 249–264). Does the same result hold for the primes 2 and 3?

Contributor: P. Flavell

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