Every finite group admits a just finite presentation
Group Theory
2026-05-12 v1 Artificial Intelligence
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.
Cite
@article{arxiv.2605.10402,
title = {Every finite group admits a just finite presentation},
author = {Marc Lackenby},
journal= {arXiv preprint arXiv:2605.10402},
year = {2026}
}
Comments
5 pages. Significant assistance was provided by the AI co-mathematician tool developed by Google DeepMind