Standard

Embeddings of quandles into groups. / Bardakov, Valeriy; Nasybullov, Timur.

In: Journal of Algebra and its Applications, Vol. 19, No. 7, 2050136, 01.07.2020.

Research output: Contribution to journal › Article › peer-review

Harvard

Bardakov, V & Nasybullov, T 2020, 'Embeddings of quandles into groups', Journal of Algebra and its Applications, vol. 19, no. 7, 2050136. https://doi.org/10.1142/S0219498820501364

APA

Bardakov, V., & Nasybullov, T. (2020). Embeddings of quandles into groups. Journal of Algebra and its Applications, 19(7), [2050136]. https://doi.org/10.1142/S0219498820501364

Vancouver

Bardakov V, Nasybullov T. Embeddings of quandles into groups. Journal of Algebra and its Applications. 2020 Jul 1;19(7):2050136. doi: 10.1142/S0219498820501364

Author

Bardakov, Valeriy ; Nasybullov, Timur. / Embeddings of quandles into groups. In: Journal of Algebra and its Applications. 2020 ; Vol. 19, No. 7.

BibTeX

@article{454ff27c105b45108899bf27ad7422ee,
title = "Embeddings of quandles into groups",
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.",
keywords = "enveloping group, free product, Quandle",
author = "Valeriy Bardakov and Timur Nasybullov",
year = "2020",
month = jul,
day = "1",
doi = "10.1142/S0219498820501364",
language = "English",
volume = "19",
journal = "Journal of Algebra and its Applications",
issn = "0219-4988",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "7",

}

RIS

TY - JOUR

T1 - Embeddings of quandles into groups

AU - Bardakov, Valeriy

AU - Nasybullov, Timur

PY - 2020/7/1

Y1 - 2020/7/1

N2 - 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.

AB - 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.

KW - enveloping group

KW - free product

KW - Quandle

UR - http://www.scopus.com/inward/record.url?scp=85086856911&partnerID=8YFLogxK

U2 - 10.1142/S0219498820501364

DO - 10.1142/S0219498820501364

M3 - Article

AN - SCOPUS:85086856911

VL - 19

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

SN - 0219-4988

IS - 7

M1 - 2050136

ER -

ID: 25615544