Writing Commutators of Commutators as Products of Cubes

TL;DR

This paper explores rewriting commutators of commutators as products of cubes, reducing the known upper bound from 60 to 14 using coset enumeration techniques.

Contribution

It introduces a new method utilizing coset enumeration to significantly lower the number of cubes needed to express commutators of commutators.

Findings

Rewrote commutators of commutators as 14 cubes

Used coset enumeration to optimize the rewriting process

Reduced the upper bound from 60 to 14 cubes

Abstract

It is known that commutators of commutators can be written as products of cubes, with the current upper bound on the number of cubes being 60. We discuss how proofs extracted via coset enumeration can be used to investigate this problem, and exhibit a rewriting using only 14 cubes.