On non-isomorphic universal sofic groups

TL;DR

This paper proves that there are uncountably many non-isomorphic universal sofic groups, confirming a conjecture by Simon Thomas and advancing the understanding of the diversity of sofic groups.

Contribution

It establishes the existence of 2^{}} non-isomorphic universal sofic groups, resolving a long-standing conjecture.

Findings

There are 2^{}} non-isomorphic universal sofic groups.

The result confirms the conjecture of Simon Thomas.

It significantly expands the known landscape of sofic groups.

Abstract

We show that there are $2^{\aleph_0}$ non-isomorphic universal sofic groups. This proves a conjecture of Simon Thomas.