Levin's conjecture for an equation of length nine

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.