Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4659247 | Topology and its Applications | 2012 | 7 Pages |
Abstract
An action of a group G on a topological space X is called minimal if for every point x∈X, the orbit Gx of x is dense in X. A connected and locally connected compact metric space which contains no simple closed curve is called a dendrite. In this paper, it is shown that if a group G acts minimally on a nondegenerate dendrite, then G must contain a free noncommutative subgroup. This is an extension of a Margulisʼ theorem for minimal group actions on the circle.
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