English

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.

Keywords

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