Abstract
For infinite discrete groups, Effros introduced the notion of inner amenability which gives a new classification of discrete groups. The inner amenability is a considerably weaker condition than amenability, but closely related to the quite deep property Γ of groups. In this paper the author investigates the structures of inner amenable groups by theoretical set theory. A sequence of characterizations of inner amenable groups is given here by developing the well-known Folner's conditions for amenable locally compact groups.
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References
Effros, E.G.,Property Γ and inner amenability, Proc. Amer. Math. Soc.,47 (1975), 483–486.
Folner, E.,On groups with full Banach mean value, Math. Scand.,3m (1955) 243–254.
Leptin, H.,On locally compact groups with invariant means, Proc. Amer. Math. Soc.,19(1968) 489–494
Pier, L.-P.,Amenable Locally Compact Groups, John Wiley and Sons Inc., New York, 1984.
Yuan C.K.,Inner amenable groups and some induced C *-algebra properties, Acta Math. Sinica, New Series,5(1989), 165–169.
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This work is partly supported by the National Science Foundation of China.
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Yuan, C.K. Structural properties of inner amenable groups. Acta Mathematica Sinica 8, 236–242 (1992). https://doi.org/10.1007/BF02582912
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DOI: https://doi.org/10.1007/BF02582912