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arXiv · 2605.10402

Every finite group admits a just finite presentation

Marc Lackenby
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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.

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Marc Lackenby. 2026-05-11. Every finite group admits a just finite presentation. https://arxiv.org/abs/2605.10402

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