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, in particular proving a conjecture of Bardakov, Neshchadim and Yadav on the number of skew braces of order 2pq for primes q > p ≥ 3.

中文翻译：

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squarefree 顺序斜括号

让n ≥ 1是一个无平方整数，并且让米,一种是两组顺序n. 使用我们先前关于在无平方度域的 Galois 扩展上枚举 Hopf-Galois 结构的结果，我们确定具有乘法群的斜括号（直到同构）的数量米和添加剂组一种. 作为一个应用，我们列举了阶数是三个不同素数的乘积的斜括号，特别是证明了 Bardakov、Neshchadim 和 Yadav 关于阶斜括号数的猜想2pq对于素数q > p ≥ 3.