MF-property for countable discrete groups

We say that a group has an MF-property if it can be embedded in the group of unitary elements of the C*-algebra ΠMn/⊕Mn. In the present paper we prove the MF-property for the Baumslag group 〈a,b|aab=a2〉\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\langle {a,b|{a^{{a^b}}} = {a^2}} \right\rangle $$\end{document} and also some general assertions concerning this property.