Work

The synchronisation hierarchy via coherent configurations

Year: 2026

Type: article

Abstract: We describe the spreading property for finite transitive permutation groups in terms of properties of their associated coherent configurations, in much the same way that separating and synchronising groups can be described via properties of their orbital graphs. We also show how the other properties in the synchronisation hierarchy naturally fit inside this framework. This combinatorial description allows for more efficient computational tools, and we deduce that every spreading permutation group of degree at most 8191 is a Q I-group. We also consider design-orthogonality more generally for noncommutative homogeneous coherent configurations.

Source: Linear Algebra and its Applications

DOI: 10.1016/j.laa.2026.01.013

Authors: John Bamberg, Jesse Lansdown

Institutions: The University of Western Australia, Tohoku University

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,230

Funders: University of Canterbury, University of Western Australia, Australian Research Council