On partial groups of small order

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.

v2: 24 pages; extended coskeletality theorem from degree 2 to degree k >= 2; added clarifying details and minor corrections throughout. comments still welcome!