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1 results

  • Transitive simple subgroups of wreath products in product action

  • Part of
  • Robert W. Baddeley, Cheryl E. Praeger, Csaba Schneider
  • Journal:
    Journal of the Australian Mathematical Society / Volume 77 / Issue 1 / August 2004
    Published online by Cambridge University Press:
    09 April 2009, pp. 55-72
    Print publication:
    August 2004
    • Article
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  • 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.