Solving a group equation of length nine

2020/08/19 by Muhammad Akram, Akram, Muhammad Saeed, Maira Amjid +1
Mathematics · #20E06 #20F05 #57M05 #FOS: Mathematics #Functional Equations Stability Results #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2008.09508

openalex publication_date 2020/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Levin conjecture was proposed by Levin in 1962 which conjectures the solvability of any group equation with coefficients in a torsion free group. The Levin conjecture is recently shown to hold for group equations of length seven by weight test and curvature distribution. These methods are applied on a group equation of length nine to explore the validity of Levin conjecture. It is found that the Levin conjecture has an affirmative answer for this equation modulo some exceptional cases.

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