Modularity of the lattice of Baer $n$-multiply $\sigma$-local formations

Let $\sigma$ be a partition of the set of all prime numbers into a union of pairwise disjoint subsets. Using the idea of multiple localization due to A. N. Skiba, we introduce the notion of a Baer $n$-multiply $\sigma$-local formation of finite groups. It is proved that with respect to inclusion $\subseteq$, the collection of all such formations form a complete algebraic modular lattice. Thereby we generalize the result obtained by A. N. Skiba and L. A. Shemetkov in [Ukr. Math. J., 52, No. 6, 783–797 (2000)].