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

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.

arXiv comment21 pages; introduction expanded and some remarks added based on referee's suggestions

References in corpus (7)

• Skew braces and the Yang-Baxter equation
• Non-existence of Hopf-Galois structures and bijective crossed homomorphisms
• On the solvability of regular subgroups in the holomorph of a finite solvable group
• On the multiple holomorph of a finite almost simple group
• Hopf-Galois structures on finite extensions with almost simple Galois group
• Hopf-Galois structures on finite extensions with quasisimple Galois group
• Hopf-Galois structures on cyclic extensions and skew braces with cyclic multiplicative group

Cited by in corpus (1)

• Normalizer Quotients of Symmetric Groups and Inner Holomorphs