Automorphism groups of relatively free groups of infinite rank: a survey

TL;DR

This survey reviews various properties of automorphism groups of relatively free groups of infinite rank, including tameness, primitivity, and the Bergman property, summarizing key theoretical insights.

Contribution

It provides a comprehensive overview of automorphism group properties for relatively free groups of infinite rank, highlighting recent developments and open problems.

Findings

Analysis of tameness and primitivity in automorphism groups

Discussion of the small index property and Bergman property

Summary of open questions and future research directions

Abstract

The paper is intended to be a survey on some topics within the framework of automorphisms of a relatively free groups of infinite rank. We discuss such properties as tameness, primitivity, small index, Bergman property, and so on.