Skew Braces of Squarefree Order

2019/10/17 by Alabdali, Ali A., Byott, Nigel P. · 1 citation
#12F10 #16T25 #16Y99 #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1910.07814

Abstract

Let n ≥ 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.

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