2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70727We 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. DedicataGroup Theory20F65; 20F69text