Transitive simple subgroups of wreath products in product action

• Autores: Cheryl E. Praeger, Csaba Schneider, Robert W. Baddeley
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 77, Nº 1, 2004, págs. 55-72
• Idioma: inglés
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• Resumen

  • 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.