Groups with undecidable word problem and almost quadratic Dehn function

TL;DR

This paper constructs a finitely presented group that has an undecidable word problem but exhibits an almost quadratic Dehn function on infinitely many positive integers, highlighting complex interactions between decision problems and geometric properties.

Contribution

It introduces a novel example of a finitely presented group with an undecidable word problem and a nearly quadratic Dehn function on an infinite subset, advancing understanding of group complexity.

Findings

Existence of a finitely presented group with undecidable word problem

Dehn function bounded by quadratic on an infinite set

Highlights complex relationship between decision problems and geometric group properties

Abstract

We construct a finitely presented group with undecidable word problem and with Dehn function bounded by a quadratic function on an infinite set of positive integers.