Using EDTOL systems to solve some equations in the solvable Baumslag-Solitar groups

We investigate the solution sets to equations in the solvable Baumslag-Solitar groups BS(1, k), k >= 2, and show that these sets are represented by EDTOL languages in some cases. In particular, we prove that the multiplication table of such a group forms an EDTOL language with respect to a specific natural normal form for group elements.(c) 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).