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arXiv · 1807.08329

Frobenius groups of automorphisms with almost fixed point free kernel

Gülin Ercan·İsmail Ş. Güloğlu
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Abstract

Let $FH$ be a Frobenius group with kernel $F$ and complement $H$, acting coprimely on the finite solvable group $G$ by automorphisms. We prove that if $C_{G}(H)$ is of Fitting length $n$ then the index of the $n$-th Fitting subgroup $F_{n}(G)$ in $G$ is bounded in terms of $|C_{G}(F)|$ and $|F|.$ This generalizes a result of Khukhro and Makarenko \cite{k-m} which handles the case $n=1.$

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Gülin Ercan, İsmail Ş. Güloğlu. 2018-07-22. Frobenius groups of automorphisms with almost fixed point free kernel. https://arxiv.org/abs/1807.08329

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