On amenability of groups generated by homogeneous automorphisms and their cracks.

We investigate the recently obtained condition [] for amenability of groups generated by bounded automorphisms of a spherically homogeneous rooted tree together with our group construction [] based on the notion of a homogeneous automorphism and its crack. We establish the general condition answering the question when a group generated by homogeneous automorphisms and their cracks is amenable. We apply this result to the universal construction from [], providing finitely generated, amenable groups, which are dense in infinitely iterated, permutational wreath products of transitive, Abelian groups. [ABSTRACT FROM AUTHOR]