Abstract
A result of amenability of some automorphism groups of a spherically homogeneous rooted tree of bounded valency is given. It is used to construct uncountably many amenable groups of non-uniform exponential growth. Their Cayley graphs can be made arbitrary close to that of some groups of intermediate growth. Yet those groups are not in the class SG of subexponentially amenable groups.
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Brieussel, J. Amenability and non-uniform growth of some directed automorphism groups of a rooted tree. Math. Z. 263, 265–293 (2009). https://doi.org/10.1007/s00209-008-0417-3
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DOI: https://doi.org/10.1007/s00209-008-0417-3