Embeddable partial groups
Group Theory
2026-03-12 v2 Algebraic Topology
Category Theory
Abstract
We record a folklore theorem that says a partial group embeds in a group if and only if each word has at most one possible multiplication, regardless of choice of parenthesization. We further investigate the partial groups which are exemplars of non-embeddability. Finally we show that a partial groupoid embeds in a groupoid if and only if its reduction embeds in a group.
Cite
@article{arxiv.2601.19772,
title = {Embeddable partial groups},
author = {Philip Hackney and Justin Lynd and Edoardo Salati},
journal= {arXiv preprint arXiv:2601.19772},
year = {2026}
}
Comments
13 pages. v2: add alternate characterization of degree of universal counterexamples to section 3 (and other minor adjustments)