The automorphism groups of relatively free groups of infinite rank

TL;DR

This survey explores recent algebraic and model-theoretic findings on automorphism groups of relatively free groups with infinite rank, focusing on topology, generators, automorphism descriptions, and logical theories.

Contribution

It compiles recent advances in understanding the structure and properties of automorphism groups of infinite rank relatively free groups, integrating algebraic and model-theoretic perspectives.

Findings

Analysis of topological structures of automorphism groups

Descriptions of generating sets for automorphisms

Insights into the expressive power of first-order theories

Abstract

A survey article that presents some recent algebraic and model-theoretic results on the automorphism groups of relatively free groups of infinite rank. The topics include topological aspects, generating sets, descripition of automorpisms and expressive power of the first-order theories.