Sofic groups and dynamical systems. (English) Zbl 1148.37302
Summary: Sofic groups were first defined by M. Gromov as a common generalization of amenable groups and residually finite groups. We discuss this new class and especially its relationship to an old problem in topological dynamics of W. Gottschalk on surjunctive groups.
MSC:
37B05 | Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) |
37B10 | Symbolic dynamics |
54H20 | Topological dynamics (MSC2010) |
43A07 | Means on groups, semigroups, etc.; amenable groups |
20F65 | Geometric group theory |
20E26 | Residual properties and generalizations; residually finite groups |