Geodesic
Nilpotent length of a finite group admitting a Frobenius group of automorphisms with fixed-point-free kernel
Algebra i logika, Tome 49 (2010) no. 6, pp. 819-833

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Suppose that a finite group $G$ admits a Frobenius group $FH$ of automorphisms with kernel $F$ and complement $H$ such that the fixed-point subgroup of $F$ is trivial, i.e., $C_G(F)=1$, and the orders of $G$ and $H$ are coprime. It is proved that the nilpotent length of $G$ is equal to the nilpotent length of $C_G(H)$ and the Fitting series of the fixed-point subgroup $C_G(H)$ coincides with a series obtained by taking intersections of $C_G(H)$ with the Fitting series of $G$.
Mots-clés : Frobenius group, automorphism, soluble group
Keywords: finite group, nilpotent length, Fitting series. 
@article{AL_2010_49_6_a6,
     author = {E. I. Khukhro},
     title = {Nilpotent length of a~finite group admitting {a~Frobenius} group of automorphisms with fixed-point-free kernel},
     journal = {Algebra i logika},
     pages = {819--833},
     publisher = {mathdoc},
     volume = {49},
     number = {6},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2010_49_6_a6/}
}
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E. I. Khukhro. Nilpotent length of a finite group admitting a Frobenius group of automorphisms with fixed-point-free kernel. Algebra i logika, Tome 49 (2010) no. 6, pp. 819-833. http://geodesic.mathdoc.fr/item/AL_2010_49_6_a6/