Intransitive Cartesian decompositions preserved by innately transitive permutation groups

2004/05/13 by Robert W. Baddeley, Cheryl E. Praeger, Baddeley, Robert W. +3
Mathematics · #05C25 #05C90 #20B05 #20B15 #20B25 #20B35 #20D40 #Advanced Topology and Set Theory #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:05C25 #msc:05C90 #msc:20B05 #msc:20B15 #msc:20B25 #msc:20B35 #msc:20D40

paper · pdf · doi:10.48550/arxiv.math/0405241

to be submitted

openalex publication_date 2004/05/13 · arxiv created 2004/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

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• Innately transitive subgroups of wreath products in product action
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• Group Embedding into Wreath Products: Cartesian Decomposition Approach
• Transitive simple subgroups of wreath products in product action