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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 (s. [5]). 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 (s. 1.6) of simple groups; therefore the Derived classes are a natural generalization of the classes of π-groups. Finally we study the lattice properties of the normal Schunck classes relative to a class of groups.
Lafuente López, Julio. "Los retículos de las clases de Schunck normales y de las clases derivadas.." Revista Matemática Hispanoamericana 39.2-3 (1979): 70-86. <http://eudml.org/doc/39757>.
@article{LafuenteLópez1979, author = {Lafuente López, Julio}, journal = {Revista Matemática Hispanoamericana}, keywords = {Grupos; Retículos; homomorph; normal Schunck class; derived classes; simple sections; projectors}, language = {spa}, number = {2-3}, pages = {70-86}, title = {Los retículos de las clases de Schunck normales y de las clases derivadas.}, url = {http://eudml.org/doc/39757}, volume = {39}, year = {1979}, }
TY - JOUR AU - Lafuente López, Julio TI - Los retículos de las clases de Schunck normales y de las clases derivadas. JO - Revista Matemática Hispanoamericana PY - 1979 VL - 39 IS - 2-3 SP - 70 EP - 86 LA - spa KW - Grupos; Retículos; homomorph; normal Schunck class; derived classes; simple sections; projectors UR - http://eudml.org/doc/39757 ER -