Ali A. Alabdali

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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…