172 research outputs found

    Transitive simple subgroups of wreath products in product action

    Full text link
    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.Comment: Submitte

    Arithmetic results on orbits of linear groups

    Full text link
    Let pp be a prime and GG a subgroup of GLd(p)GL_d(p). We define GG to be pp-exceptional if it has order divisible by pp, but all its orbits on vectors have size coprime to pp. We obtain a classification of pp-exceptional linear groups. This has consequences for a well known conjecture in representation theory, and also for a longstanding question concerning 1/2-transitive linear groups (i.e. those having all orbits on nonzero vectors of equal length), classifying those of order divisible by pp.Comment: slight revisions after referee's comment
    • …
    corecore