Skew braces with no proper left ideals

Abstract

A skew brace $A=(A,\cdot ,\circ )$ is said to be \textit{left-simple} if $A\ne 1$ and it has no left ideal other than $1$ and $A$. The purpose of this paper is to give a partial classification of the finite left-simple skew braces. A result of Stefanello and Trappeniers implies that finite left-simple skew braces correspond precisely to minimal Hopf--Galois structures on finite Galois extensions of fields.

Cited by in corpus (1)

• On the triviality and non-triviality of the automorphism group of a skew brace