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PreprintCC BY 4.0arXiv

Every finite group admits a just finite presentation

  • Marc Lackenby
Open at sourcePDFDOICite

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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Cite

BibTeXRIS
BibTeX
@misc{lackenby2026every,
  title = {{Every finite group admits a just finite presentation}},
  author = {Marc Lackenby},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2605.10402},
  eprint = {2605.10402},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.10402},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Every finite group admits a just finite presentation
AU  - Marc Lackenby
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2605.10402
UR  - https://arxiv.org/abs/2605.10402
AB  - 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.
ER  -