Intransitive Cartesian decompositions preserved by innately transitive permutation groups

Details Intransitive Cartesian decompositions preserved by innately transitive permutation groups Intransitive Cartesian decompositions preserved by innately transitive permutation groups

2004-05-13

arxiv.org/abs/math/0405241v2

Mathematics

Group Theory

to be submitted

Scientific paper

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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