Automorphism groups of saturated structures; a review

TL;DR

This review summarizes two decades of research on automorphism groups of saturated structures, focusing on properties like the small index property, reconstructability, and strong automorphisms.

Contribution

It consolidates key results and themes in the study of automorphism groups of saturated structures over the past twenty years.

Findings

Analysis of the small index property in various cases

Insights into reconstructing structures from automorphism groups

Discussion of the subgroup of strong automorphisms

Abstract

We will review the main results concerning the automorphism groups of saturated structures which were obtained during the two last decades. The main themes are: the small index property in the countable and uncountable cases; the possibility of recovering a structure or a significant part of it from its automorphism group; the subgroup of strong automorphisms.