English

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

Logic 2022-03-11 v3 Group Theory

Abstract

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 MM, Polish group GG of permutations of MM, and n1n \geq 1, GG has a comeager nn-diagonal conjugacy class iff the family of all nn-tuples of GG-extendable bijections between finitely generated substructures of MM, has the joint embedding property and the weak amalgamation property. We characterize limits of weak Fra\"{i}ss\'{e} classes that are not homogenizable. Finally, we investigate 11- and 22-diagonal conjugacy classes in groups of ball-preserving bijections of certain ordered ultrametric spaces.

Keywords

Cite

@article{arxiv.1908.09494,
  title  = {Remarks on weak amalgamation and large conjugacy classes in non-archimedean groups},
  author = {Maciej Malicki},
  journal= {arXiv preprint arXiv:1908.09494},
  year   = {2022}
}
R2 v1 2026-06-23T10:56:32.218Z