标题： 单生成元斜Brace和不可分解的集合理论Yang-Baxter方程解 显示英文标题

标题： One-generator skew braces and indecomposable set-theoretic solutions to the Yang-Baxter equation

摘要： 我们研究了一类由单个生成元所满足的杨-巴克方程解，推广了一些关于对合解和多重置换解的近期成果。 此外，我们展示了杨-巴克方程的不可分解解与有限单生成偏体之间的精确关系，从而对Agata和Alicja Smoktunowicz提出的问题给出了肯定的回答。 在最后一部分，我们将结果应用于对合情形，并展示了一些涉及小规模解的数值结果。 显示英文摘要

摘要： We study the class of one-generator solutions to the Yang-Baxter equation, extending some recent results concerning the classes of involutive and multipermutation solutions. Moreover we show the precise relationship between indecomposable solutions to the Yang-Baxter equation and finite one-generator skew braces, giving a positive answer to a question posed by Agata and Alicja Smoktunowicz. In the last part, we apply our results to the involutive case, and we present some numerical results involving solutions of small size.