MF-property for countable discrete groups

TL;DR

This paper investigates the MF-property in countable discrete groups, demonstrating that the Baumslag group possesses this property and exploring its fundamental characteristics.

Contribution

It proves that the Baumslag group has the MF-property and examines some permanent features of MF-groups.

Findings

Baumslag group has MF-property

Established permanence properties of MF-groups

Contributed to understanding of MF-property in discrete groups

Abstract

In this article we study MF-property for countable discrete groups, i.e. groups which admit embedding into unitary group of $C^*$-algebra $\prod M_n/\oplus M_n$. We prove that Baumslag group $\langle a,b|a^{a^b}=a^2\rangle$ has MF-property and check some permanent facts about MF-groups.