Non-abelian simple groups which occur as the type of a Hopf-Galois structure on a solvable extension

TL;DR

This paper classifies all finite non-abelian simple groups that can serve as the type of a Hopf-Galois structure on a solvable extension, linking group theory and algebraic structures.

Contribution

It provides a complete list of non-abelian simple groups that appear as additive groups of skew braces with solvable multiplicative groups.

Findings

Identifies all non-abelian simple groups relevant to Hopf-Galois structures

Connects skew brace structures with solvable extensions

Offers a classification result for algebraic structures in Galois theory

Abstract

We determine the finite non-abelian simple groups which occur as the type of a Hopf-Galois structure on a solvable extension. In the language of skew braces, our result gives a complete list of finite non-abelian simple groups which occur as the additive group of a skew brace with solvable multiplicative group.