Free subgroups of dendrite homeomorphism group

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.