Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2025

Dimension and partial groups

Résumé

A partial group with $n+1$ elements is, when regarded as a symmetric simplicial set, of dimension at most $n$. This dimension is $n$ if and only if the partial group is a group. As a consequence of the first statement, finite partial groups are genuinely finite, despite being seemingly specified by infinitely much data. In particular, finite partial groups have only finitely many im-partial subgroups. We also consider dimension of partial groupoids.

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hal-04630052 , version 1 (01-07-2024)
hal-04630052 , version 2 (25-06-2025)

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Philip Hackney, Rémi Molinier. Dimension and partial groups. Proceedings of the American Mathematical Society, 2025, 154 (2), pp.469-476. ⟨10.1090/proc/17423⟩. ⟨hal-04630052v2⟩
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