# Jordan groups and homogeneous structures

@inproceedings{BradleyWilliams2014JordanGA, title={Jordan groups and homogeneous structures}, author={David Bradley-Williams}, year={2014} }

A permutation group G acting transitively on a set Ω is a Jordan group if there is a proper subset Γ ⊂ Ω, subject to some non-triviality conditions, such that the pointwise stabiliser in G of Ω \ Γ is transitive on Γ. Such sets Γ are called Jordan sets for G. Here we study infinite primitive Jordan groups which are automorphism groups of first order relational structures. We find a model theoretic application in classifying the reducts of an infinite family of semilinearly ordered partial…

## 2 Citations

### Jordan permutation groups and limits of 𝐷-relations

- MathematicsJournal of Group Theory
- 2021

Abstract We construct via Fraïssé amalgamation an 𝜔-categorical structure whose automorphism group is an infinite oligomorphic Jordan primitive permutation group preserving a “limit of…

### On limits of betweenness relations

- Mathematics
- 2023

Abstract We give a flexible method for constructing a wide variety of limits of betweenness relations. This unifies work of Adeleke, who constructed a Jordan group preserving a limit of betweenness…

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