Algebraic entropy of elementary amenable groups
arXiv:math/0404075
Abstract
We prove that any finitely generated elementary amenable group of zero (algebraic) entropy contains a nilpotent subgroup of finite index or, equivalently, any finitely generated elementary amenable group of exponential growth is of uniformly exponential growth. We also show that 0 is an accumulation point of the set of entropies of elementary amenable groups.
20 pages; to appear in Geom. Dedicata