Satellites and products of ωσ-fibered Fitting classes

A Fitting class F = omega sigma R(f, phi) = (G : O-omega (G) is an element of f (omega') and G(phi(omega boolean AND sigma i)) is an element of f (omega boolean AND sigma(i)) for all omega boolean AND sigma(i) is an element of omega sigma(G)) is called an omega sigma-fibered Fitting class with omega sigma-satellite f and omega sigma-direction phi. By phi(0) and phi(1) we denote the directions of an omega sigma-complete and an omega sigma-local Fitting class, respectively. Theorem 1 describes a minimal omega sigma-satellite of an omega sigma-fibered Fitting class with omega sigma-direction phi, where phi(0) <= phi. Theorem 2 states that the Fitting product of two omega sigma-fibered Fitting classes is an omega sigma-fibered Fitting class for omega sigma-directions phi such that phi(0) <= phi <= phi(1). Results for omega sigma-complete and omega sigma-local Fitting classes are obtained as corollaries of the theorems. Theorem 3 describes a maximal internal omega sigma-satellite of an omega sigma-complete Fitting class. An omega sigma L-satellite is defined as an omega sigma-satellite f such that f (omega boolean AND sigma(i)) is the Lockett class for all omega boolean AND sigma(i) is an element of omega sigma. Theorem 4 describes the maximal internal omega sigma L-satellite of an omega sigma-local Fitting class. Questions of the study of lattices and further study of products and critical omega sigma-fibered Fitting classes are posed in the conclusion.