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A proof of Brauer's k(B)k(B)-conjecture at the prime two

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

Contributed by Qiyue Tang ↗

Version 1 / Nov 13, 2026 / CC BY 4.0

Abstract

We prove that every 22-block of a finite group has at most as many ordinary irreducible characters as the order of its defect groups.

Author comments: 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.

Provenance statement

GPT-6-Pro was used during approximately 29 hours of documented research sessions on Brauer's $k(B)$-conjecture. This paper presents the prime-two part of that investigation. GPT-6-Pro was also used to review the mathematical arguments and polish the manuscript. A review by Rethlas-OSV will be added in a subsequent update.

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Version history

  1. v1 · 102 pagesSubmitted by Qiyue TangI 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 13, 2026