2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75034It is relatively easy to construct a finitely generated group with infinite asymptotic dimension: the restricted wreath product of $\mathbb{Z}$ by $\mathbb{Z}$ provides an example. In light of this, it becomes interesting to consider the rate of growth of the asymptotic dimension function of a group. Loosely speaking, we measure the dimension on $λ$-scale and let $λ$ increase to infinity to recover the asymptotic dimension. In this paper we consider how the asymptotic dimension function is affected by different constructions involving groups.14 pages, no figuresGroup TheoryPrimary: 20F69, Secondary 20E06, 20E22, 20F65text