Remarks on weak amalgamation and large conjugacy classes in non-archimedean groups

We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure M , Polish group G of permutations of M , and n ≥ 1 , G has a comeager n -diagonal conjugacy class iff the family of all n -tuples of G -extendable bijections between finitely generated substructures of M , has the joint embedding property and the weak amalgamation property. We characterize limits of weak Fraïssé classes that are not homogenizable. Finally, we investigate 1- and 2-diagonal conjugacy classes in groups of ball-preserving bijections of certain ordered ultrametric spaces.