# Skew braces of squarefree order

@article{Alabdali2019SkewBO, title={Skew braces of squarefree order}, author={Ali Abdulqader Bilal Alabdali and Nigel P. Byott}, journal={arXiv: Rings and Algebras}, year={2019} }

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 fields of squarefree degree, we determine the number of skew braces (up to isomorphism) with multiplicative group $M$ and additive group $A$. As an application, we enumerate skew braces whose order is the product of three distinct primes.

## 9 Citations

### Skew braces of size pq

- Mathematics
- 2019

Abstract We construct all skew braces of size pq (where p > q are primes) by using Byott’s classification of Hopf–Galois extensions of the same degree. For there exists only one skew brace which is…

### Skew braces of size $p^2q$

- Mathematics
- 2019

In this paper we enumerate the skew braces of size pq for p, q odd primes by the classification of regular subgroups of the holomorph of the groups of size pq. In particular, we provide explicit…

### Hopf Galois structures on field extensions of degree twice an odd prime square and their associated skew left braces

- Mathematics
- 2020

### Skew Braces of Size p2 q I: Abelian Type

- MathematicsAlgebra Colloquium
- 2022

This is the first part of a series of two articles. In this paper we enumerate and classify the left braces of size [Formula: see text], where[Formula: see text] and [Formula: see text] are distinct…

### Hopf-Galois structures on cyclic extensions and skew braces with cyclic multiplicative group

- MathematicsProceedings of the American Mathematical Society, Series B
- 2022

. Let G and N be two ﬁnite groups of the same order. It is well-known that the existences of the following are equivalent. ( a ) a Hopf-Galois structure of type N on any Galois G -extension ( b ) a…

### Indecomposable solutions of the Yang-Baxter equation with permutation group of sizes $pq$ and $p^2q$

- Mathematics
- 2022

. In this paper we study the problem of classiﬁcation of indecomposable solutions of the Yang-Baxter equation. Using a scheme proposed by Bachiller, Cedó, and Jespers, and recent advances in the…

### Affine structures on groups and semi-braces

- Mathematics
- 2022

We introduce aﬃne structures on groups and show they form a category equivalent to that of semi-braces. In particular, such a new description of semi-braces includes that presented by Rump for…

### Skew braces of size p2q II: Non-abelian type

- MathematicsJournal of Algebra and Its Applications
- 2020

In this paper we enumerate the skew braces of non-abelian type of size [Formula: see text] for [Formula: see text] primes with [Formula: see text] by the classification of regular subgroups of the…

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- Mathematics
- 2019

Abstract We construct all skew braces of size pq (where p > q are primes) by using Byott’s classification of Hopf–Galois extensions of the same degree. For there exists only one skew brace which is…

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Braces are generalizations of radical rings, introduced by Rump to study involutive non-degenerate set-theoretical solutions of the Yang-Baxter equation (YBE). Skew braces were also recently…