Geodesic
$\mathrm{MF}$-Property for Countable Discrete Groups
Matematičeskie zametki, Tome 102 (2017) no. 2, pp. 231-246.

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We say that a group has an $\mathrm{MF}$-property if it can be embedded in the group of unitary elements of the $C^*$-algebra $\prod M_n/\bigoplus M_n$. In the present paper we prove the $\mathrm{MF}$-property for the Baumslag group ${\langle a,b \mid a^{a^b}=a^2\rangle}$ and also some general assertions concerning this property.
Keywords: countable groups, representations, $C^*$-algebras, Baumslag group. 
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     title = {$\mathrm{MF}${-Property} for {Countable} {Discrete} {Groups}},
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A. I. Korchagin. $\mathrm{MF}$-Property for Countable Discrete Groups. Matematičeskie zametki, Tome 102 (2017) no. 2, pp. 231-246. http://geodesic.mathdoc.fr/item/MZM_2017_102_2_a5/

[1] J. Carrión, M. Dadarlat, C. Eckhardt, “On groups with quasidiagonal $C^*$-algebras”, J. Funct. Anal., 265:1 (2013), 135–152 | DOI | MR | Zbl

[2] A. Tikuisis, S. White, W. Winter, “Quasidiagonality of nuclear $C^*$-algebras”, Ann. of Math. (2), 185:1 (2017), 229–284 | MR | Zbl

[3] V. M. Manuilov, A. S. Mishchenko, “Almost, asymptotic and Fredholm representations of discrete groups”, Acta Appl. Math., 68:1 (2001), 159–210 | DOI | MR | Zbl

[4] M. Dadarlat, “Group quasi-representations and almost flat bundles”, J. Noncommut. Geom., 8:1 (2014), 163–178 | DOI | MR | Zbl

[5] V. Capraro, M. Lupini, Introduction to Sofic and Hyperlinear groups and Connes' Embedding Conjecture, Lectures Notes in Math., 2136, Springer-Verlag, Cham, 2015 | DOI | MR | Zbl

[6] B. Blackadar, E. Kirchberg, “Generalized inductive limits of finite-dimensional $C^*$-algebras”, Math. Ann., 307:3 (1997), 343–380 | MR | Zbl

[7] P. H. Kropholler, “Baumslag-Solitar groups and some other groups of cohomological dimention two”, Comment. Math. Helv., 65:4 (1990), 547–558 | DOI | MR | Zbl

[8] N. P. Brown, N. Ozawa, $C^*$-Algebras and Finite Dimensional Approximations, Grad. Stud. Math., 88, Amer. Math. Soc., Providence, RI, 2008 | MR | Zbl

[9] D. Avitzour, “Free products of $C^*$-algebras”, Trans. Amer. Math. Soc., 271:2 (1982), 423–435 | MR | Zbl

[10] Q. Li, J. Shen, “A note on unital full amalgamated free products of RFD $C^*$-algebras”, Illinois J. Math., 56:2 (2012), 647–659 | MR | Zbl

[11] G. Elek, E. Szabó, “On sofic groups”, J. Group Theory, 9:2 (2006), 161–171 | DOI | MR | Zbl

[12] V. G. Pestov, “Hyperlinear and sofic groups: a brief guide”, Bull. Symbolic Logic, 14:4 (2008), 449–480 | DOI | MR | Zbl

[13] D. N. Azarov, D. Tedzho, “Ob approksimiruemosti svobodnogo proizvedeniya grupp s ob'edinennoi podgruppoi kornevym klassom grupp”, Nauch. tr. Ivanovsk. gos. un-ta. Matem., 2002, no. 5, 6–10

[14] K. W. Gruenberg, “Residual properties of infinite soluble groups”, Proc. London Math. Soc. (3), 7 (1957), 29–62 | DOI | MR | Zbl