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PreprintCC BY 4.0arXiv

A Note on the OpenAI Construction of Counterexamples to the Kaplansky Direct-Finiteness Conjecture

  • Andrei Jaikin-Zapirain
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Abstract

We give a human-readable exposition of OpenAI's construction of a group algebra in characteristic two that is not directly finite. We then adapt the argument to show that, for every prime p, there exists a hyperbolic group Gp such that 𝔽p[Gp] is not directly finite.

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Cite

BibTeXRIS
BibTeX
@misc{jaikinzapirain2026note,
  title = {{A Note on the OpenAI Construction of Counterexamples to the Kaplansky Direct-Finiteness Conjecture}},
  author = {Andrei Jaikin-Zapirain},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08268},
  eprint = {2611.08268},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08268},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Note on the OpenAI Construction of Counterexamples to the Kaplansky Direct-Finiteness Conjecture
AU  - Andrei Jaikin-Zapirain
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08268
UR  - https://arxiv.org/abs/2611.08268
AB  - We give a human-readable exposition of OpenAI's construction of a group algebra in characteristic two that is not directly finite. We then adapt the argument to show that, for every prime p, there exists a hyperbolic group G_p such that 𝔽_p[G_p] is not directly finite.
ER  -