On groups with EDT0L word problem

TL;DR

This paper investigates the class of groups with EDT0L word problems, proving the infinite cyclic group does not belong to this class and exploring properties that such groups must have, advancing toward classifying all groups with EDT0L word problems.

Contribution

It establishes that the infinite cyclic group is not EDT0L and shows that having an EDT0L word problem implies the group is torsion, progressing toward a full classification.

Findings

Infinite cyclic group is not EDT0L

Groups with EDT0L word problem are torsion

EDT0L property is invariant under generating set changes and subgroup formation

Abstract

We prove that the word problem for the infinite cyclic group is not EDT0L, and obtain as a corollary that a finitely generated group with EDT0L word problem must be torsion. In addition, we show that the property of having an EDT0L word problem is invariant under change of generating set and passing to finitely generated subgroups. This represents significant progress towards the conjecture that all groups with EDT0L word problem are finite (i.e. precisely the groups with regular word problem).