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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2510.00081 |
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| _version_ | 1866911187204046848 |
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| author | Arai, Hiroshi |
| author_facet | Arai, Hiroshi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00081 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Elementary Proof of the Nonexistence of Tarski Monster Groups of Exponent 3 Arai, Hiroshi Group Theory 2020: Primary 20F50, Secondary 20E32, 20F45 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. |
| title | An Elementary Proof of the Nonexistence of Tarski Monster Groups of Exponent 3 |
| topic | Group Theory 2020: Primary 20F50, Secondary 20E32, 20F45 |
| url | https://arxiv.org/abs/2510.00081 |