Pseudofinite primitive permutation groups acting on one-dimensional sets
Volume 250 / 2020
Fundamenta Mathematicae 250 (2020), 117-149
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.
