有限困境的分类
Toward a classification of finite quandles
摘要：
本文总结了一个学生团队（前三位作者）在第四位作者的指导下在2005年KSU REU“头脑风暴和巡回演讲”会议上取得的实质性新成果。主要结果是用“半不交并”运算表示的quandle的分解定理，证明了所有有限quandle通过迭代半不交并正则地分解为连通子quandle，以及具有指定内自同构群的有限连通quandle的结构定理.后一个定理提出了一种新的方法来分类有限连通quandles。
英文摘要：
This paper summarizes substantive new results derived by a student team (the first three authors) under the direction of the fourth author at the 2005 session of the KSU REU ``Brainstorming and Barnstorming''. The main results are a decomposition theorem for quandles in terms of an operation of `semidisjoint union' showing that all finite quandles canonically decompose via iterated semidisjoint unions into connected subquandles, and a structure theorem for finite connected quandles with prescribe inner automorphism group. The latter theorem suggests a new approach to the classification of finite connected quandles.
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