N. Byott

activity

20062026

most citedSolubility Criteria for Hopf-Galois Structures

16 citations · 30 across the 15 of their papers we have counts for

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6 papers · 1 filter

math.RA2024

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…

math.RA2019

Skew Braces of Squarefree Order

Ali A. Alabdali, Nigel P. Byott

Let $n \geq 1$ be a squarefree integer, and let $M$ , $A$ be two groups of order $n$ . Using our previous results on the enumeration of Hopf-Galois structures on Galois extensions of…

math.RA2019

Hopf-Galois Structures of Squarefree Degree

Ali A. Alabdali, Nigel P. Byott

Let $n$ be a squarefree natural number, and let $G$ , $Γ$ be two groups of order $n$ . We determine the number of Hopf-Galois structures of type $G$ admitted by a Galois extension of…

math.RA2017

Counting Hopf-Galois Structures on Cyclic Field Extensions of Squarefree Degree

Ali A. Alabdali, Nigel P. Byott

We investigate Hopf-Galois structures on a cyclic field extension $L / K$ of squarefree degree $n$ . By a result of Greither and Pareigis, each such Hopf-Galois structure corresponds…

math.RA2014★ 16 cited

Solubility Criteria for Hopf-Galois Structures

Nigel P. Byott

Let $L / K$ be a finite Galois extension of fields with group $Γ$ . Associated to each Hopf-Galois structure on $L / K$ is a group $G$ of the same order as the Galois group $Γ$ . The typ…

math.RA2012

Nilpotent and abelian Hopf-Galois structures on field extensions

Nigel P. Byott

Let $L / K$ be a finite Galois extension of fields with group $Γ$ . When $Γ$ is nilpotent, we show that the problem of enumerating all nilpotent Hopf-Galois structures on $L / K$ can be…