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arXiv · 2605.26199

On partial groups of small order

Philip Hackney
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Abstract

We explain a computer enumeration of all partial groups (in the sense of Chermak) of order at most 10. An accompanying dataset contains a full list, consisting of 123,650 partial groups of order at most 9 and 178,937,003 partial groups of order 10; the paper itself contains a complete list of indecomposable partial groups of order at most 5. Inspection of the data led us to conjecture and then prove two results: that indecomposable partial groups of dimension two less than their order are precisely skeleta of groups of that order, and partial groups of (higher Segal) degree at most 2 are 2-coskeletal.

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Philip Hackney. 2026-07-07. On partial groups of small order. https://arxiv.org/abs/2605.26199

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