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 CG(H) is of Fitting length n then the index of the n-th Fitting subgroup Fn(G) in G is bounded in terms of |CG(F)| and |F|. This generalizes a result of Khukhro and Makarenko [6] which handles the case n=1.
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