Group cocycles and the ring of affiliated operators
نویسندگان
چکیده
In this article we study cocycles of discrete countable groups with values in 2G and the ring of affiliated operators UG. We clarify properties of the first cohomology of a group G with coefficients in 2G and answer several questions from De Cornulier et al. (Transform. Groups 13(1):125–147, 2008). Moreover, we obtain strong results about the existence of free subgroups and the subgroup structure, provided the group has a positive first 2-Betti number. We give numerous applications and examples of groups which satisfy our assumptions.
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