Every finite group admits a just finite presentation

2026/05/11 by Marc Lackenby · 1 voice
Computer Science · Mathematics · #cs.AI #math.GR

paper · pdf · doi:10.48550/arxiv.2605.10402

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.

Citations

• AI co-mathematician: Accelerating mathematicians with agentic AI
• On the structure of just infinite profinite groups
• Subgroups of finite index and the just infinite property

Discussions

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