Local factorisations of nonlocal Fitting classes

We consider general rules of constructing of local products of the Fitting classes with the use of nonlocal factors determined by the minimal elements of the Lockett section. We give a simple method to construct local Fitting classes which are factorised by nonlocal Fitting classes of some classes of $\pi$-groups and $\pi'$-groups. Applying the class $\mathfrak B$, we simplify the procedure of construction of a nonlocal factor in the local product. It is shown that in the construction of the local product the nonlocal factor for the appropriate set of primes $\pi$ is the Fitting class of the form $\mathfrak B_*\mathfrak S_\pi$, where $\mathfrak B_*$ is the minimal element of the Lockett section of the class $\mathfrak B$. In this paper, we consider only finite solvable groups.