16 citations · 30 across the 15 of their papers we have counts for
20 papers
Magma Automorphisms and Quasi-Linear Cycle Sets
Nigel P. Byott, Edgar Jasko
Rump asked in 2016 whether every finite quasi-linear cycle set is retractible. We reinterpret this question in terms of automorphisms of certain pointed magmas, and propose a conje…
On a family of simple skew braces
Nigel P. Byott
Several constructions have been given for families of simple braces, but few examples are known of simple skew braces which are not braces. In this paper, we exhibit the first exam…
On the number of quaternion and dihedral braces and Hopf--Galois structures
Nigel P. Byott, Fabio Ferri
We prove a conjecture of Guarnieri and Vendramin on the number of braces of a given order whose multiplicative group is a generalised quaternion group. At the same time, we give a…
On Insoluble Transitive Subgroups in the Holomorph of a Finite Soluble Group
Nigel P. Byott
A question of interest both in Hopf-Galois theory and in the theory of skew braces is whether the holomorph of a finite soluble group can contain an insoluble…
Hopf-Galois Structures on Non-Normal Extensions of Degree Related to Sophie Germain Primes
Nigel P. Byott, Isabel Martin-Lyons
We consider Hopf-Galois structures on separable (but not necessarily normal) field extensions of squarefree degree . If is the normal closure of then $G=\mathr…
Skew Braces of Squarefree Order
Ali A. Alabdali, Nigel P. Byott
Let be a squarefree integer, and let , be two groups of order . Using our previous results on the enumeration of Hopf-Galois structures on Galois extensions of…