Examples of Hyperlinear Groups without Factorization Property
نویسنده
چکیده
In this note we give an example of a group which is locally embeddable into finite groups (in particular it is initially subamenable, sofic and hence hyperlinear) but does not have Kirchberg’s factorization property. This group provides also an example of a sofic Kazhdan group which is not residually finite, answering a question from [ES05]. We also give an example of a group which is not initially subamenable but hyperlinear. Finally, we point out a mistake in [Kir94, Corollary 1.2 (v)⇒(i)] and [Kir93, Corollary 7.3(iii)] and provide an example of a group which does not have the factorization property and is still a subgroup of a connected finitedimensional Lie group.
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متن کاملREFERENCES TO THE COURSE ”FINITE-DIMENSIONAL APPROXIMATION PROPERTIES OF FINITE GROUPS” References
[4] Lev Glebsky and Luis Manuel Rivera, Sofic groups and profinite topology on free groups, J. Algebra 320 (2008), no. 9, 3512-3518. [2] Misha Gromov, Endomorphisms of symbolic algebraic varieties, J. Eur. Math. Soc. (JEMS) 1 (1999), no. 2, 109-197. [3] Gábor Elek and Endre Szabó, Hyperlinearity, essentially free actions and Linvariants. The sofic property, Math. Ann. 332 (2005), no. 2, 421-441...
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