Work

On a family of simple skew braces

Year: 2025

Type: article

Abstract: Several constructions have been given for families of simple braces, but few examples are known of simple skew braces which are not braces. In this paper, we exhibit the first example of an infinite family of simple skew braces which are not braces and which do not arise from nonabelian simple groups. More precisely, we show that, for any primes [Formula: see text], [Formula: see text] such that [Formula: see text] divides [Formula: see text], there are exactly two simple skew braces (up to isomorphism) of order [Formula: see text].

Source: Journal of Algebra and Its Applications

DOI: 10.1142/s0219498826502300

Author: Nigel P. Byott

Institution: University of Exeter

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Award: Hopf-Galois Theory and Skew Braces