Levin's conjecture for an equation of length nine

TL;DR

This paper extends the verification of Levin's conjecture to a specific group equation of length nine, confirming its validity except for some exceptional cases.

Contribution

It demonstrates that Levin's conjecture holds for a particular length nine group equation, advancing the understanding beyond previous lengths.

Findings

Levin's conjecture is valid for the considered length nine equation

The proof is modulo some exceptional cases

Extends known results from lengths up to seven and eight

Abstract

Levin's conjecture has been established to hold true for group equations of length up to seven. Recently, it is shown that Levin's conjecture is also true (modulo exceptional cases) for some group equations of length eight and nine. In this paper we consider a group equation of length nine and show that the Levin's conjecture is true for this equation modulo some exceptional cases.