3 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.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
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…