Embeddings of quandles into groups
Embeddings of quandles into groups
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将 qudle 嵌入到组中
DOI：
10.1142/s0219498820501364
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发表时间：
2019
影响因子：
0.8
通讯作者：
T. Nasybullov
中科院分区：
文献类型：
--
作者：
V. Bardakov;T. Nasybullov
在本文中，我们介绍了quandles的新结构。对于组[公式：我们构造了一个quandle [Formula：see text]，称之为[Formula：see text]-quandle，并研究了这个quandle的性质。特别地，我们证明了如果[Formula：see text]是quandle，使得从[Formula：see text]到[Formula：see text]的包络群[Formula：see text]的自然映射[Formula：see text]是单射的，则[Formula：see text]是[Formula：see text]的适当群[Formula：see text]和[Formula：see text]的子集[Formula：see text]的[Formula：see text]-quandle。见正文]。此外，我们还介绍了quandles的自由积，并研究了[公式：见文本]-quandles的这种构造。此外，我们还对所有具有包络群的有限quandles进行了分类[公式：见正文]。
In this paper, we introduce the new construction of quandles. For a group [Formula: see text] and a subset [Formula: see text] of [Formula: see text] we construct a quandle [Formula: see text] which is called the [Formula: see text]-quandle and study properties of this quandle. In particular, we prove that if [Formula: see text] is a quandle such that the natural map [Formula: see text] from [Formula: see text] to the enveloping group [Formula: see text] of [Formula: see text] is injective, then [Formula: see text] is the [Formula: see text]-quandle for an appropriate group [Formula: see text] and a subset [Formula: see text] of [Formula: see text]. Also we introduce the free product of quandles and study this construction for [Formula: see text]-quandles. In addition, we classify all finite quandles with enveloping group [Formula: see text].