English

On partial groups of small order

Group Theory 2026-05-27 v1 Algebraic Topology Combinatorics

Abstract

There are 123,650 partial groups of order at most 9 and 178,937,003 partial groups of order 10. We explain a computer enumeration of these results and provide a complete list of indecomposable partial groups of order at most 5. We also indicate results that were discovered through computational experiments.

Cite

@article{arxiv.2605.26199,
  title  = {On partial groups of small order},
  author = {Philip Hackney},
  journal= {arXiv preprint arXiv:2605.26199},
  year   = {2026}
}

Comments

23 pages, comments welcome!