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Intransitive Cartesian decompositions preserved by innately transitive permutation groups

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

We study Cartesian decompositions of sets that are acted upon intransitively by innately transitive permutation groups. We prove that such groups have at most three orbits on such a decomposition. A consequence of this result is that if $G$ is an innately transitive subgroup of a wreath product in product action then the natural projection of $G$ into the top group has at most 2 orbits.

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Robert W. Baddeley, Cheryl E. Praeger, Csaba Schneider. 2004-06-22. Intransitive Cartesian decompositions preserved by innately transitive permutation groups. https://arxiv.org/abs/math/0405241

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