The generalized Fitting height of a finite group G is the least number h = h∗(G) such that F ∗ h (G) = G, where the F ∗ i (G) is the generalized Fitting series: F ∗ 1 (G) = F ∗(G) and F ∗ i+1(G) is the inverse image of F ∗(G/F ∗ i (G)). It is proved that if G admits a soluble group of automorphisms A of coprime order, then h∗(G) is bounded in terms of h∗(CG(A)), where CG(A) is the fixed-point s...
