Embeddings of quandles into groups

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5 Citations (Scopus)

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 GQ from Q to the enveloping group GQ 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 a&2. ;copy 2020 World Scientific Publishing Company.

Original languageEnglish
Article number2050136
Number of pages20
JournalJournal of Algebra and its Applications
Volume19
Issue number7
DOIs
Publication statusPublished - 1 Jul 2020

Keywords

  • enveloping group
  • free product
  • Quandle

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