The nonsoluble length λ(G)\documentclass[12pt]{minimal}
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\begin{document}$$\lambda (G)$$\end{document} of a finite group G\documentclass[12pt]{minimal}
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\begin{document}$$G$$\end{document} is defined as the minimum number of nonsoluble factors in a normal series each of whose factors either is soluble or is a direct product of non-abelian simple groups. The generalized Fitting height of a finite group G\documentclass[12pt]{minimal}
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\begin{document}$$G$$\end{document} is the least number h=h∗(G)\documentclass[12pt]{minimal}
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\begin{document}$$h=h^*(G)$$\end{document} such that Fh∗(G)=G\documentclass[12pt]{minimal}
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\begin{document}$$F^*_h(G)=G$$\end{document}, where F1∗(G)=F∗(G)\documentclass[12pt]{minimal}
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\begin{document}$$F^*_1(G)=F^*(G)$$\end{document} is the generalized Fitting subgroup, and Fi+1∗(G)\documentclass[12pt]{minimal}
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\begin{document}$$F^*_{i+1}(G)$$\end{document} is the inverse image of F∗(G/Fi∗(G))\documentclass[12pt]{minimal}
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\begin{document}$$F^*(G/F^*_{i}(G))$$\end{document}. It is proved that if a finite group G=AB\documentclass[12pt]{minimal}
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\begin{document}$$G=AB$$\end{document} is factorized by two subgroups of coprime orders, then the nonsoluble length of G\documentclass[12pt]{minimal}
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\begin{document}$$G$$\end{document} is bounded in terms of the generalized Fitting heights of A\documentclass[12pt]{minimal}
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\begin{document}$$A$$\end{document} and B\documentclass[12pt]{minimal}
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\begin{document}$$B$$\end{document}. It is also proved that if, say, B\documentclass[12pt]{minimal}
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\begin{document}$$B$$\end{document} is soluble of derived length d\documentclass[12pt]{minimal}
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\begin{document}$$d$$\end{document}, then the generalized Fitting height of G\documentclass[12pt]{minimal}
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\begin{document}$$G$$\end{document} is bounded in terms of d\documentclass[12pt]{minimal}
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\begin{document}$$d$$\end{document} and the generalized Fitting height of A\documentclass[12pt]{minimal}
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\begin{document}$$A$$\end{document}.
