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Does someone know example of group (countable, discrete) which can not be embedded (monomorphism) into $$ U(\prod M_n/\oplus M_n)$$ unitary group of universal MF-algebra? Or example of group which can not be embedded into $U(A)$ - unitary group of some AF-algebra $A$? It seems, that notions of MF-group and AF-group (groups which admit embeddings, we are mentioned above) are similar to notion of hyperlinearity of group. Does someone know interesting facts about MF-groups and AF-groups?

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  • $\begingroup$ I think this question has been asked before on MO? $\endgroup$
    – Yemon Choi
    Dec 7, 2015 at 22:36
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    $\begingroup$ This is an open problem. $\endgroup$
    – Andreas Thom
    Dec 8, 2015 at 9:57
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    $\begingroup$ Related to this question, but not exactly the same mathoverflow.net/questions/221703/… $\endgroup$
    – Yemon Choi
    Dec 10, 2015 at 14:00

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