On the Brouwer lattices of $\omega$-fibered formations of finite groups

Only finite groups and classes of finite groups are considered. A class of groups is a set of groups that, with each group $G$, contains all groups isomorphic to $G$. In this paper we study formations, i.e. classes of groups that are closed under homomorphic images and subdirect products. The purpose of this paper is to research the lattice properties of $\omega$-fibered formations where $\omega$ is a non-empty set of primes. Sufficient conditions, under which the Brouwer lattice $\omega \delta F (\frak F)$ of all $\omega$-fibered subformations with an arbitrary direction $\delta$ of a given formation $\frak F$ is a Stone lattice, are established. As corollaries of the main theorem, results for $\omega$-local, local formations and other types of formations imply.