Minimum satellite of $\tau$-closed $n$-fold $\Omega$-foliated Fitting class

A multitude of groups containing isomorphic ones to each group is called a class of groups. Among the classes of finite groups formations, Fitting classes, and Schunk classes are distinguished. The study of classes of finite groups in our country was begun in the works of L.A. Shemetkov, where the role of the function in the study of formation was shown, different types of formations were defined. In recent years, A.N. Skiba, S.F. Kamornikov and M.V. Selkin considered subgroup functors, established a connection between them and classes of groups, introduced the notion of closedness of a class of groups with respect to a subgroup functor. You can trace the successful study of formations, closed respective of subgroup functors. However, Fitting classes in this field have been studied very little. Therefore research on the Fitting classes closed respective of subgroup functors is highly relevant. In this work, we introduced the concept of coregular and coradical subgroup functor, and the description was obtained of the structure of the only minimum satellite of an $n$-fold foliated Fitting class closed respective of subgroup functor. To prove the fundamental theorems a method of colliding particles was used. The work also resulted in obtaining a number of properties of $n$-fold foliated Fitting classes closed respective of subgroup functor, and namely, the property of multiplicity, crossing, dependency between a Fitting class and its satellite.