Using EDT0L systems to solve some equations in the solvable Baumslag-Solitar groups

Abstract

We investigate the solution sets to equations in the solvable Baumslag-Solitar groups $BS(1,k)$, $k\ge 2$, and show that these sets are represented by EDT0L languages in some cases. In particular, we prove that the multiplication table of such a group forms an EDT0L language with respect to a specific natural normal form for group elements.

30 pages, 1 figure