We explain how the germ of the structure group of a cycle set decomposes as a product of its Sylow-subgroups, and how this process can be reversed to construct cycle sets from ones with coprime classes. We study Dehornoy’s class associated to a cycle set, and conjecture a bound that we prove in a specific case. We combine the use of braces and a monomial representation, in particular to answer a question by Dehornoy on retrieving the Garside structure without a theorem of Rump, while also retrieving said theorem.

中文翻译：

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Yang-Baxter 方程的集合论解的 Dehornoy 类和 Sylows

我们解释了循环集的结构群的萌芽如何分解为其 Sylow 子群的乘积，以及如何反转该过程以从具有互质类的循环集构造循环集。我们研究与循环集相关的 Dehornoy 类，并推测我们在特定情况下证明的界限。我们结合使用大括号和单项式表示，特别是回答 Dehornoy 提出的关于在没有 Rump 定理的情况下检索 Garside 结构的问题，同时检索所述定理。