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 c1asses composed a complete and distributive lattice antiisomorphic to the lattice composed by the Derived c1asses (s. [5]). It begins with a first section of machinery which establishes that the Derived c1asses are precisely the c1asses of groups G such that every simple section of G appartains to a o-c1osed class (s. 1.6) of simple groups; therefore the Derived c1asses are a natural generalization of the c1asses of pi-groups. Finally we study the lattice properties of the normal Schunck c1asses relative to a c1ass of groups.