Work

The non-synchronizing primitive groups of degree up to 624

Year: 2025

Type: article

Abstract: We describe the methods and results of a classification of the non-synchronizing primitive permutation groups of degree up to 624. We make use of theory and computation to determine the primitive groups of degree up to 624 that are non-separating, which is a necessary, and very often sufficient, condition for a primitive group to be non-synchronizing, and determine exactly which of these non-separating groups are non-synchronizing. A new infinite sequence of non-synchronizing graphs is discovered and new examples of non-separating, but synchronizing, groups are found.

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2025.08.003

Author: Leonard H. Soicher

Institution: Queen Mary University of London

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,310

Funders: Queen Mary University of London, Engineering and Physical Sciences Research Council