发表机构
Nara University of Education（奈良教育大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过研究群作用相关的拟群构造，建立了有限拟群的Cayley型嵌入定理，并利用对称群的自然作用构造出能嵌入所有$n$元拟群的泛拟群。
AI 中文摘要
拟群（quandle）是一种代数系统，可视为群中共轭运算的推广。本文建立了有限拟群的Cayley型嵌入定理。为此，我们研究了与群作用相关的一种拟群构造，并确定了其基本结构性质。将该构造应用于对称群的自然作用，我们得到了一个拟群，使得每个基数为$n$的拟群都能嵌入其中。
英文摘要
A quandle is an algebraic system that can be regarded as a generalization of the conjugation operation in groups. We study a quandle construction associated with group actions and determine its structural properties, including its inner automorphism group, connected components, and subquandles. As a principal application, we establish a Cayley-type embedding theorem for finite quandles. Applying the construction to the natural action of the symmetric group, we obtain, for each $n$, a single quandle into which every quandle of cardinality $n$ embeds.
