A note on torsion length

TL;DR

This paper constructs a 2-generator recursively presented group with infinite torsion length and explores its properties within solvable and hyperbolic groups.

Contribution

It introduces a novel example of a 2-generator group with infinite torsion length and analyzes its behavior in different group classes.

Findings

Constructed a 2-generator group with infinite torsion length.

Analyzed the group's properties in solvable and hyperbolic contexts.

Provided insights into torsion length in various group types.

Abstract

We construct a 2-generator recursively presented group with infinite torsion length. We also explore the construction in the context of solvable and word-hyperbolic groups.