Pseudofinite primitive permutation groups acting on one-dimensional sets

Tingxiang Zou Fundamenta Mathematicae MSC: Primary 03C20; Secondary 20B15. DOI: 10.4064/fm799-12-2019 Published online: 31 January 2020

Abstract

Working in a theory with an integer-valued dimension on interpretable sets, we classify pseudofinite definably primitive permutation groups acting on one-dimensional sets which satisfy a version of chain condition on centralizers and on pointwise stabilizers. This generalizes the classification of pseudofinite definably primitive permutation groups acting on a rank $1$ set in supersimple theories of finite rank, due to Elwes et al. (2011), to supersimple theories of infinite rank.

Authors

  • Tingxiang ZouInstitut Camille Jordan
    Université Lyon I
    21, avenue Claude Bernard
    69622 Villeurbanne, France
    e-mail

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