Construction of a Regularly Exhausting Sequence for Groups with Subexponential Growth

It is proved that every group with subexponential growth contains a regularly exhausting sequence with polynomial growth. A consequence is answering in the negative Question 14.27 in “The Kourovka Notebook” – namely, a continuum of non-isomorphic 2-generated groups are constructed which each have a regularly exhausting sequence with polynomial growth and which are but not groups with polynomial growth.