Hopf-Galois structures of isomorphic type on a non-abelian characteristically simple extension

Abstract

Let $L/K$ be a finite Galois extension whose Galois group $G$ is non-abelian and characteristically simple. Using tools from graph theory, we shall give a closed formula for the number of Hopf-Galois structures on $L/K$ with associated group isomorphic to $G$.

arXiv comment16 pages; revised based on the referee's comments. Accepted for publication

References in corpus (1)

• Non-existence of Hopf-Galois structures and bijective crossed homomorphisms

Cited by in corpus (4)

• Rota-Baxter groups, skew left braces, and the Yang-Baxter equation
• Hopf-Galois structures on finite extensions with almost simple Galois group
• Hopf-Galois structures on finite extensions with quasisimple Galois group
• Finite skew braces with isomorphic non-abelian characteristically simple additive and circle groups