A sofic group away from amenable groups

TL;DR

This paper presents an example of a sofic group that cannot be approximated by amenable groups, highlighting a distinction within group theory classifications.

Contribution

It provides the first known example of a sofic group that is not a limit of amenable groups, advancing understanding of group approximation properties.

Findings

Identifies a sofic group outside the class of limits of amenable groups

Demonstrates the existence of non-approximable sofic groups

Contributes to the classification of group approximation types

Abstract

We give an example of a sofic group, which is not a limit of amenable groups.