Constructions of torsion-free countable, amenable, weakly mixing groups. (English) Zbl 1382.20034
Summary: In this note, we construct countable, torsion-free, amenable, weakly mixing groups, which answer a question of V. Bergelson. Some results related to verbal subgroups and crystallographic groups are also presented.
MSC:
| 20E26 | Residual properties and generalizations; residually finite groups |
| 20E22 | Extensions, wreath products, and other compositions of groups |
| 20F60 | Ordered groups (group-theoretic aspects) |
| 22D10 | Unitary representations of locally compact groups |
| 37A15 | General groups of measure-preserving transformations and dynamical systems |
| 43A07 | Means on groups, semigroups, etc.; amenable groups |
Keywords:
weakly mixing group; WM group; minimally almost periodic group; variety of groups; verbal subgroup; torsion-free group; wreath product; orderable groupReferences:
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