Publication: Los retículos de las clases de Schunck normales y de las clases derivadas
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1979
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Real Sociedad Matemática Española;Consejo Superior de Investigaciones Científicas. Instituto "Jorge Juan" de Matemáticas
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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.
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