Title: On the existence of complements of residuals of finite group
Abstract: L.A. Shemetkov's theorem on the complementability of the F-residual of a finite group is developed in the article. For an ω-local Fitting formation F, it is proved that, if G is a finite group generated by subnormal subgroups A1,...,An, the subgroups A1F,...,AnF are ω-soluble, and Sylow p-subgroups of A1F,...,AnF are abelian for every p∈ω, then each ωF-normalizer of G is an ω-complement of GF in G.