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- Title
Embeddings of quandles into groups.
- Authors
Bardakov, Valeriy; Nasybullov, Timur
- Abstract
In this paper, we introduce the new construction of quandles. For a group G and a subset A of G we construct a quandle Q (G , A) which is called the (G , A) -quandle and study properties of this quandle. In particular, we prove that if Q is a quandle such that the natural map Q → G Q from Q to the enveloping group G Q of Q is injective, then Q is the (G , A) -quandle for an appropriate group G and a subset A of G. Also we introduce the free product of quandles and study this construction for (G , A) -quandles. In addition, we classify all finite quandles with enveloping group ℤ 2 .
- Subjects
EMBEDDINGS (Mathematics); CONSTRUCTION
- Publication
Journal of Algebra & Its Applications, 2020, Vol 19, Issue 7, pN.PAG
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498820501364