Primitive pseudo-finite permutation groups of finite SU-rank

Ulla Karhumäki; Nicholas Ramsey

Primitive pseudo-finite permutation groups of finite SU-rank

Logic 2025-11-25 v2 Group Theory

Authors: Ulla Karhumäki , Nicholas Ramsey

Abstract

We study definably primitive pseudo-finite permutation groups of finite $SU$ -rank. We show that if $(G,X)$ is such a permutation group, then the rank of $G$ can be bounded in terms of the rank of $X$ , providing an analogue of a theorem of Borovik and Cherlin in the setting of definably primitive permutation groups of finite Morley rank.

Keywords

primitive permutation groups pseudo-finite groups SU-rank definable groups Borovik-Cherlin theorem

Cite

@article{arxiv.2504.08501,
  title  = {Primitive pseudo-finite permutation groups of finite SU-rank},
  author = {Ulla Karhumäki and Nicholas Ramsey},
  journal= {arXiv preprint arXiv:2504.08501},
  year   = {2025}
}

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