标题： 共轭子拟群的良置对合 显示英文标题

标题： Good involutions of conjugation subquandles

摘要： 由Taniguchi提出，具有良好对合的拟群的分类是一个具有挑战性的问题，并且在表面纽结理论中有应用。 我们针对共轭拟群的子拟群，包括所有核心拟群，解决了这个问题。 我们还研究了忠实rack的良好对合。 特别是，我们得到了这些族中rack的良好对合数量的精确界限。 作为我们结果的应用，我们实现了计算共轭拟群和核心拟群的所有良好对合的群论算法；我们提供了到阶数23的数据。 作为另一个应用，我们构造了无限多个连通的、非对合的对称拟群族。 我们还使用计算机搜索对阶数8以内的对称和Legendrian rack、拟群和kei进行了分类。 最后，我们展示了rack和Legendrian rack之间的范畴等价关系，该等价关系诱导了对合rack、Legendrian kei和对称kei之间的等价关系。 显示英文摘要

摘要： Posed by Taniguchi, the classification of quandles with good involutions is a difficult question with applications to surface-knot theory. We address this question for subquandles of conjugation quandles, including all core quandles. We also study good involutions of faithful racks. In particular, we obtain sharp bounds on the number of good involutions of racks in these families. As an application of our results, we implement group-theoretic algorithms that compute all good involutions of conjugation quandles and core quandles; we provide data for those up to order 23. As another application, we construct infinite families of connected, noninvolutive symmetric quandles. We also classify symmetric and Legendrian racks, quandles, and kei up to order 8 using a computer search. Finally, we exhibit an equivalence of categories between racks and Legendrian racks that induces an equivalence between involutory racks, Legendrian kei, and symmetric kei.