arXiv cs.AI· Marc Lackenby·· 11 小时前AI 评分45
每个有限群都存在“just finite”表现：Google DeepMind AI 协作数学工具助力解决 Kourovka Notebook 问题 21.10
Every finite group admits a just finite presentation
AI 导读
数学家证明每个有限群都存在“just finite”表现，即删去任一关系即得到无限群的表现，从而正面解决了 Kourovka Notebook 问题 21.10 这一公开猜想。该工作得到 Google DeepMind 开发的 AI 协作数学工具的重要协助，论文共 7 页，已被 Journal of Group Theory 接收。
正文 · 原文
Abstract:A finite presentation < X | R > of a finite group is called `just finite' if removing any relation from R results in a presentation for an infinite group. It has been an open question (Kourovka Notebook, Problem 21.10) whether every finite group admits such a presentation. We resolve this conjecture in the affirmative.
| Comments: | Significant assistance was provided by the AI co-mathematician tool developed by Google DeepMind. v2: 7 pages, incorporates referee's comments and improvements. Accepted by the Journal of Group Theory |
| Subjects: | Group Theory (math.GR); Artificial Intelligence (cs.AI) |
| MSC classes: | 20F05, 20D99, 20E06, 22D55 |
| Cite as: | arXiv:2605.10402 [math.GR] |
| (or arXiv:2605.10402v2 [math.GR] for this version) | |
| https://doi.org/10.48550/arXiv.2605.10402 arXiv-issued DOI via DataCite |
Submission history
From: Marc Lackenby [view email]
[v1]
Mon, 11 May 2026 11:42:08 UTC (6 KB)
[v2]
Wed, 4 Nov 2026 09:57:27 UTC (7 KB)
来源：arXiv cs.AI · arxiv.org