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arXiv · 2510.00081

An Elementary Proof of the Nonexistence of Tarski Monster Groups of Exponent 3

Hiroshi Arai
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Abstract

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.

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Hiroshi Arai. 2025-09-30. An Elementary Proof of the Nonexistence of Tarski Monster Groups of Exponent 3. https://arxiv.org/abs/2510.00081

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