The Ω-foliated formations and Fitting classes of finite groups

A new functional approach to the study of classes of groups is proposed, resulting in description of all formations and Fitting classes of finite groups in the language of functions. The Ω-foliated formations ΩF(f, φ) and Ω-foliated Fitting classes ΩF(f, φ) with satellite f and direction φ are constructed. To each satellite f there corresponds an infinite set of various directions φ. One direction leads to the previously considered Ω-composite formations. In this way the Ω-canonical and Ω-free formations and Fitting classes are obtained. For a fixed direction φ the structure of the minimal satellite f is obtained. © VSP 2001.