Hopf-Galois structures on finite extensions with quasisimple Galois group

Abstract

Let $L/K$ be a finite Galois extension of fields with Galois group $G$. It is known that $L/K$ admits exactly two Hopf-Galois structures when $G$ is non-abelian simple. In this paper, we extend this result to the case when $G$ is quasisimple.

arXiv commentAccepted version. Sections 4.1 and 4.2 have been swapped

References in corpus (8)

• 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 Arising From Groups with Unique Subgroup of Order p
• Hopf-Galois structures of isomorphic type on a non-abelian characteristically simple extension
• Hopf-Galois structures on a Galois $S_n$-extension

Cited by in corpus (2)

• Hopf-Galois structures on cyclic extensions and skew braces with cyclic multiplicative group
• Non-abelian simple groups which occur as the type of a Hopf-Galois structure on a solvable extension