# Conjugating automorphisms of graph products: Kazhdan's property (T) and SQ-universality

## TL;DR

This paper characterizes when the group of conjugating automorphisms of a graph product of groups has Kazhdan's property (T) and exhibits SQ-universality, revealing deep structural properties of these automorphism groups.

## Contribution

It provides a precise characterization of conditions under which conjugating automorphism groups of graph products have property (T) and are SQ-universal.

## Key findings

- Conjugating automorphism groups satisfy property (T) under specific conditions.
- They are SQ-universal in certain cases.
- The paper offers a complete classification for these properties.

## Abstract

An automorphism of a graph product of groups is conjugating if it sends each factor to a conjugate of a factor (possibly different). In this article, we determine precisely when the group of conjugating automorphisms of a graph product satisfies Kazhdan's property (T) and when it satisfies some vastness properties including SQ-universality.