# Fitting height of a finite group with a Frobenius group of automorphisms

Khukhro, E. I. (2012) Fitting height of a finite group with a Frobenius group of automorphisms. [MIMS Preprint]

Suppose that a finite group $G$ admits a Frobenius group of automorphisms $FH$ with kernel $F$ and complement $H$ such that $F$ acts without non-trivial fixed points (that is, such that $C_G(F)=1$). It is proved that the Fitting height of $G$ is equal to the Fitting height of the fixed-point subgroup $C_G(H)$ and the Fitting series of $C_G(H)$ coincides with the intersections of $C_G(H)$ with the Fitting series of $G$. As a corollary, it is also proved that for any set of primes $\pi$ the $\pi$-length of $G$ is equal to the $\pi$-length of $C_G(H)$.