2025/09/30 by Hiraku Arai, Arai, Hiroshi
Mathematics · #2020: Primary 20F50 #20F45 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Secondary 20E32 #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2510.00081
openalex publication_date 2025/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known that Tarski monster groups of exponent~3 do not exist. Traditional proofs rely on deep structural results, such as the restricted Burnside problem, properties of the free Burnside group, or Engel-type identities, and involve substantial technical computations. In this note we give a fully elementary proof: the argument reduces to a single simple identity, expressed as a key equation, whose verification requires only a brief calculation.