Cheryl E. Praeger, Robert W. Baddeley, Csaba Schneider
Published 2002-10-04, updated 2003-03-04Version 2
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 systemsof subgroups'. These concepts, and the bijective connections between them, are explored in greater generality, with specific future applications in mind.
Innately transitive subgroups of wreath products in product action
Finite generation of iterated wreath products in product action
Three types of inclusions of innately transitive permutation groups into wreath products in product action
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