Los retículos de las clases de Schunck normales y de las clases derivadas

Abstract

All groups to be considered are finite. The main result of this paper is the following: the normal Schunck classes compose a complete and distributive lattice antiisomorphic to the lattice composed by the derived classes. It begins with a first section of machinery which establishes that the derived classes are precisely the classes of groups G such that every simple section of G appartains to a σ-closed class of simple groups; therefore the derived classes are a natural generalization of the classes of σ-groups. Finally we study the lattice properties of the normal Schunck classes relative to a class of groups.