On core quandles of groups
On core quandles of groups
复制标题
论群体的核心问题
DOI：
10.1080/00927872.2021.1874400
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发表时间：
2020
影响因子：
0.7
通讯作者：
G. Bergman
中科院分区：
文献类型：
--
作者：
G. Bergman
本文讨论了群G的quandle的定义，特别是群G的核心quandle的定义，它由群G的基础集合组成，具有二元运算。这是一个对合quandle，即，除了满足定义困境的其他恒等式之外，还满足该恒等式。群中的轨迹和对合困境中的轨迹（在前一种情况下，序列的形式以及其他特征;在后一种情况下，序列满足检查。对合量子点Q可嵌入群的核量子点的一系列必要条件。在群体中的身份认同与其核心困境之间建立了一些含义。上，下界上所需的元素的数量生成的quandle G的一个生成群。提出了几个问题。
Abstract We review the definition of a quandle, and in particular of the core quandle of a group G, which consists of the underlying set of G, with the binary operation This is an involutory quandle, i.e., satisfies the identity in addition to the other identities defining a quandle. Trajectories in groups and in involutory quandles (in the former context, sequences of the form among other characterizations; in the latter, sequences satisfying are examined. A family of necessary conditions for an involutory quandle Q to be embeddable in the core quandle of a group is noted. Some implications are established between identities holding in groups and in their core quandles. Upper and lower bounds are obtained on the number of elements needed to generate the quandle for G a finitely generated group. Several questions are posed.