CLASSIFICATION OF INFINITE PRIMITIVE JORDAN PERMUTATION-GROUPS

We prove that every infinite primitive Jordan permutation group preser ves a structure in one of a finite list of familiar families, or a lim it of structures in one of these families. The structures are: semilin ear orders ('trees') or betweenness relations induced from semilinear orders, chains of semilinear orders, points at infinity of a betweenne ss relation, linear and circular orders and the corresponding betweenn ess and separation relations, and Steiner systems. A Jordan group is a permutation group (G, Omega) such that there is a subset Gamma subset of or equal to Omega satisfying various non-triviality assumptions, w ith G((Omega/Gamma)) transitive on Gamma.