Intransitive Cartesian decompositions preserved by innately transitive permutation groups
Group Theory
2007-05-23 v2
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 is an innately transitive subgroup of a wreath product in product action then the natural projection of into the top group has at most 2 orbits.
Cite
@article{arxiv.math/0405241,
title = {Intransitive Cartesian decompositions preserved by innately transitive permutation groups},
author = {Robert W. Baddeley and Cheryl E. Praeger and Csaba Schneider},
journal= {arXiv preprint arXiv:math/0405241},
year = {2007}
}
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