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Broué's Abelian Defect Group Conjecture for 2-Blocks

Primarily AI-generated textHuman understanding: no partsmath.RT — Representation Theorymath.GR — Group Theory

Contributed by Qiyue Tang

Version 1 / Nov 11, 2026 / CC BY 4.0

Abstract

We prove that every 2-block of a finite group with an abelian defect group is splendidly Rickard equivalent to its Brauer correspondent.

Author comments: By posting this manuscript on this platform, I do not seek to assert ownership of the results or claim priority. I welcome anyone interested in preparing a finished account or checking the arguments; the eventual scholarly credit should go to those who undertake that work.

Provenance statement

GPT-6-Pro was used for 13 rounds of mathematical research, totaling approximately 90.8 hours, up to the initial completion of the proof for 2-blocks. GPT-6-Pro was also used to review the mathematical arguments and polish the manuscript. An additional review by Rethlas-OSV will be incorporated at a later stage.

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Version history

  1. v1 · 41 pagesSubmitted by Qiyue TangBy posting this manuscript on this platform, I do not seek to assert ownership of the results or claim priority. I welcome anyone interested in preparing a finished account or checking the arguments; the eventual scholarly credit should go to those who undertake that work.SupersededNov 10, 2026
  2. v2 · 48 pagesSubmitted by Qiyue Tangv2（2026/11/11）：Version 1 underwent several rounds of review and revision with GPT-6-Pro and subsequently passed the Rethlas-OSV review (GPT-6-Astra, high reasoning effort, four concurrent workers), which reported no mathematical issues. I am posting this manuscript to share the mathematical results themselves. In doing so, I do not seek to assert ownership of the results or claim priority. I welcome anyone interested in checking the arguments or preparing a finished account, and I believe the eventual scholarly credit should go to those who undertake that work.CurrentNov 11, 2026