8 problems

Let $N$ be a finite soluble group, and write … A subgroup of $\operatorname{Hol}(N)$ is regular when its natural action on $N$ is free and transitive. Byott's conjecture. Every reg…

Byott's conjecture. If $L/K$ admits a Hopf–Galois structure of soluble type, then its Galois group

Almost-classical correspondence conjecture. The almost classically Galois Hopf--Galois structures of type $N$ are exactly the Hopf--Galois structures which admit a bijective corres…

Let $L/K$ be a separable field extension of squarefree degree. Say that $L/K$ has the parallel no-HGS property if it admits a Hopf–Galois structure while a parallel extension assoc…

Let $N$ be a finite soluble group, and let $G$ be a regular subgroup of the holomorph … of $N$, meaning that $G$ acts regularly on the underlying set of $N$. Regular-subgroup solub…

Let $\Gamma$ and $\Delta$ be finite groups of the same order. Write $e(\Gamma,\Delta)$ for the number of Hopf-Galois structures on a Galois extension with Galois group $\Gamma$ and…

Let $\HI$ be the Hopf algebra constructed in the paper as the dual of the infinite torsion group underlying the profinite Hopf–Galois extension. Author's conjecture. The algebra…

Let $H$ be a bimonoid in a monoidal model category $\mathbf M$. Suppose that the category $\mathbf{Alg}_{H}$ of $H$-comodule algebras admits a model structure for which the coinvar…