- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:58
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
4
2010
1
Examples of hyperlinear groups without factorization property
Andreas
Thom
Technische Universität Dresden, DRESDEN, GERMANY
Hyperlinear group, sofic group, Kazhdan’s property (T), factorization property
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 finite-dimensional Lie group.
Group theory and generalizations
Topological groups, Lie groups
Functional analysis
General
195
208
10.4171/GGD/80
http://www.ems-ph.org/doi/10.4171/GGD/80