Every finite group admits a just finite presentation
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866916000720486400 |
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| author | Lackenby, Marc |
| author_facet | Lackenby, Marc |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10402 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Every finite group admits a just finite presentation Lackenby, Marc Group Theory Artificial Intelligence 20F05, 20D99, 20E06, 22D55 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. |
| title | Every finite group admits a just finite presentation |
| topic | Group Theory Artificial Intelligence 20F05, 20D99, 20E06, 22D55 |
| url | https://arxiv.org/abs/2605.10402 |