On satellites of $\sigma_\Omega$-foliated formations of groups

Only finite groups are considered. A class of groups is called a formation if it is closed under taking homomorphic images and subdirect products. For a nonempty class $\Omega$ of simple groups, V. A. Vedernikov defined $\Omega$-foliated formations of finite groups using two types of functions, viz., satellite functions and direction functions. Let $\sigma_\Omega$ be an arbitrary partition of the class $\Omega$. We study $\sigma_\Omega$-foliated formations, where $\sigma_\Omega$ is an arbitrary partition of the class $\Omega$ constructed by the authors of the preset paper as a natural generalization of the concept of an $\Omega$-foliated formation using A. N. Skiba's $\sigma$-methods. We prove the existence of different types of satellites of $\sigma_\Omega$-foliated formations and describe their structure.