Free subgroups of branch groups.
The main aim of the paper is to construct finitely generated branch groups on the binary tree which contain non-cyclic free subgroups. This answers three of four points of Problem 15.14 in the Kourovka Notebook. Namely: Do there exist finitely generated branch groups (a) that are non-amenable; (c) that contain the free group \(F_2\); (d) that have exponential growth? The answer to point (c) is given by Theorem 1. There exist finitely generated branch groups defined on the binary tree containing non-cyclic free subgroups. -- Further, the groups with non-cyclic free subgroup have exponential growth, and are non-amenable. These answer points (a) and (d).
scientific article; zbMATH DE number 1993477