On groups whose geodesic growth is polynomial

摘要

This note records some observations concerning geodesic growth\udfunctions. If a nilpotent group is not virtually cyclic then it has exponential\udgeodesic growth with respect to all finite generating sets. On the other hand,\udif a finitely generated group G has an element whose normal closure is abelian\udand of finite index, then G has a finite generating set with respect to which\udthe geodesic growth is polynomial (this includes all virtually cyclic groups)