Group topologies on automorphism groups of homogeneous structures

Zaniar Ghadernezhad and Javier de la Nuez González

Vol. 327 (2023), No. 1, 83–105

DOI: 10.2140/pjm.2023.327.83

Abstract

We provide sufficient conditions for the standard topology (generated by stabilizers of finite sets) on the automorphism group of a countable homogeneous structure to be minimal among all Hausdorff group topologies on the group. Under certain assumptions, such as when the structure is the Fraïssé limit of a relational class with the free amalgamation property, we are able to classify all the group topologies on the automorphism group coarser than the standard topology even when the latter is not minimal.

Keywords

minimal topological groups, automorphism groups, oligomorphic groups

Mathematical Subject Classification

Primary: 22A05, 22F50

Secondary: 03C15, 03C45, 20B27

Milestones

Received: 2 May 2023

Revised: 6 November 2023

Accepted: 6 November 2023

Published: 18 February 2024