Resumen de Transitive simple subgroups of wreath products in product action
Cheryl E. Praeger, Csaba Schneider, Robert W. Baddeley
A transitive simple subgroup of a finite symmetric group is very rarely contained in a full wreath product in product action. All such simple permutation groups are determined in this paper. This remarkable conclusion is reached after a definition and detailed examination of `Cartesian decompositions' of the permuted set, relating them to certain `Cartesian systems of subgroups'. These concepts, and the bijective connections between them, are explored in greater generality, with specific future applications in mind.
