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arXiv:2605.10402math.GR

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.

arXiv comments
5 pages. Significant assistance was provided by the AI co-mathematician tool developed by Google DeepMind
Journal reference
DOI
Subjects
math.GRGroup Theory cs.AIArtificial Intelligence

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