Overgroups of the Automorphism Group of the Rado Graph

TL;DR

This paper explores the structure of overgroups of the Rado graph's automorphism group, focusing on understanding their relationships and connections to known classes called reducts.

Contribution

It establishes links between various natural overgroups of the Rado graph's automorphism group and the class of reducts, expanding understanding of their structure.

Findings

Complete understanding of a class of overgroups (reducts)

Established connections between other overgroups and reducts

Enhanced the structural understanding of automorphism overgroups

Abstract

We are interested in overgroups of the automorphism group of the Rado graph. One class of such overgroups is completely understood; this is the class of reducts. In this article we tie recent work on various other natural overgroups, in particular establishing group connections between them and the reducts.