On complements of coradicals of finite groups

Let F be an omega-local Fitting formation, and G a finite group that can be represented in the form of a product of n subnormal subgroups whose F-coradicals are omega-soluble, and whose Sylow p-subgroups are abelian for any p is an element of omega. It is established that there exist omega-complements of the F-coradical of G. New theorems on the existence of complements of coradicals of a group are obtained as corollaries. For an omega-local formation F, conditions are established for the existence of complements and omega-complements of the F-coradical of a group in any of its extensions.