# 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}
}```
• Published 17 October 2019
• Mathematics
• arXiv: Rings and Algebras
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

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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
• Mathematics
• 2012
The main theorem of this paper is that if (N, +) is a finite abelian p-group of p-rank m where m + 1 < p, then every regular abelian subgroup of the holomorph of N is isomorphic to N . The proof
• Mathematics
• 2016
New constructions of braces on finite nilpotent groups are given and hence this leads to new solutions of the Yang–Baxter equation. In particular, it follows that if a group G of odd order is
We define a bi-skew brace to be a set \$G\$ with two group operations \$\star\$ and \$\circ\$ so that \$(G, \circ, \star)\$ is a skew brace with additive group \$(G, \star)\$ and also with additive group \$(G,
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• 2016
Braces and linear cycle sets are algebraic structures playing a major role in the classification of involutive set-theoretic solutions to the Yang-Baxter equation. This paper introduces two versions
• Mathematics
• 2017
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