On satellites of σ Ω -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 Ω of simple groups, V. A. Vedernikov defined Ω -foliated formations of finite groups using two types of functions, viz., satellite functions and direction functions. Let σ Ω be an arbitrary partition of the class Ω . We study σ Ω -foliated formations, where σ Ω is an arbitrary partition of the class Ω constructed by the authors of the preset paper as a natural generalization of the concept of an Ω -foliated formation using A. N. Skiba’s σ -methods. We prove the existence of different types of satellites of σ Ω -foliated formations and describe their structure.