collaborators

5 papers

math.GR2026

Indecomposable solutions with permutation brace of size and permutation braces of small sizes

Andrew Darlington, Magdalena Wiertel

Using the construction of Bachiller, Cedó and Jespers, we give a complete classification of the indecomposable involutive set-theoretic solutions to the Yang-Baxter equation whose…

math.GR2026

Hopf--Galois structures of cyclic type on parallel extensions of prime power degree

Andrew Darlington, Cindy Tsang

Let be any finite separable extension with normal closure . An extension is said to be $\textit{parallel to $L/K$}$ if is an intermediate field o…

math.GR2026

Constructing Hopf-Galois structures and skew bracoids of small degree

Andrew Darlington, Eamonn O'Brien

Using the fact that Hopf-Galois structures on separable extensions and skew bracoids are both intrinsically connected to transitive subgroups of the holomorph of a finite group, we…

math.GR2025

Hopf-Galois structures on separable field extensions of degree related to Cunningham chains

Andrew Darlington

The past few years have seen Hopf--Galois structures on extensions of squarefree degree studied in various contexts. The Galois case was fully explored by Alabdali and Byott in 202…

math.GR2025

Hopf-Galois structures on parallel extensions

Andrew Darlington

Let be a finite separable extension of fields of degree , and let be its Galois closure. Greither and Pareigis showed how to find all Hopf--Galois structures on $L/K…