Work

On the number of quaternion and dihedral braces and Hopf–Galois structures

Year: 2024

Type: article

Abstract: We prove a conjecture of Guarnieri and Vendramin on the number of braces of a given order whose multiplicative group is a generalised quaternion group. At the same time, we give a similar result where the multiplicative group is dihedral. We also enumerate Hopf-Galois structures of abelian type on Galois extensions with generalised quaternion or dihedral Galois group.

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2024.11.011

Authors: Nigel P. Byott, Fabio Ferri

Institution: University of Exeter

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,140

Funder: Engineering and Physical Sciences Research Council