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Transitive simple subgroups of wreath products in product action

Cheryl E. Praeger·Robert W. Baddeley·Csaba Schneider
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Abstract

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.

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Cheryl E. Praeger, Robert W. Baddeley, Csaba Schneider. 2003-03-04. Transitive simple subgroups of wreath products in product action. https://arxiv.org/abs/math/0210057

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