Automorphism groups of quandles and related groups

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Automorphism groups of quandles and related groups. / Bardakov, V.; Nasybullov, T.; Singh, M.

In: Monatshefte fur Mathematik, Vol. 189, No. 1, 01.05.2019, p. 1-21.

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

Harvard

Bardakov, V, Nasybullov, T & Singh, M 2019, 'Automorphism groups of quandles and related groups', Monatshefte fur Mathematik, vol. 189, no. 1, pp. 1-21. https://doi.org/10.1007/s00605-018-1202-y

APA

Bardakov, V., Nasybullov, T., & Singh, M. (2019). Automorphism groups of quandles and related groups. Monatshefte fur Mathematik, 189(1), 1-21. https://doi.org/10.1007/s00605-018-1202-y

Vancouver

Bardakov V, Nasybullov T, Singh M. Automorphism groups of quandles and related groups. Monatshefte fur Mathematik. 2019 May 1;189(1):1-21. doi: 10.1007/s00605-018-1202-y

Author

Bardakov, V. ; Nasybullov, T. ; Singh, M. / Automorphism groups of quandles and related groups. In: Monatshefte fur Mathematik. 2019 ; Vol. 189, No. 1. pp. 1-21.

BibTeX

@article{b1f2e71e46d04800b4bf47e11a86cf9e,

title = "Automorphism groups of quandles and related groups",

abstract = "In this paper we study various questions concerning automorphisms of quandles. For a conjugation quandle (Formula presented.) of a group G we determine several subgroups of (Formula presented.) and find necessary and sufficient conditions for these subgroups to coincide with the whole group (Formula presented.). In particular, we prove that (Formula presented.) if and only if either (Formula presented.) or G is one of the groups (Formula presented.), (Formula presented.) or (Formula presented.). For a big list of Takasaki quandles T(G) of an abelian group G with 2-torsion we prove that the group of inner automorphisms (Formula presented.) is a Coxeter group. We study automorphisms of certain extensions of quandles and determine some interesting subgroups of the automorphism groups of these quandles. Also we classify finite quandles Q with k-transitive action of (Formula presented.) for (Formula presented.).",

keywords = "Automorphism of a quandle, Braid group, Coxeter group, Enveloping group, Quandle",

author = "V. Bardakov and T. Nasybullov and M. Singh",

note = "Publisher Copyright: {\textcopyright} 2018, Springer-Verlag GmbH Austria, part of Springer Nature.",

year = "2019",

month = may,

day = "1",

doi = "10.1007/s00605-018-1202-y",

language = "English",

volume = "189",

pages = "1--21",

journal = "Monatshefte fur Mathematik",

issn = "0026-9255",

publisher = "Springer-Verlag GmbH and Co. KG",

number = "1",

}

RIS

TY - JOUR

T1 - Automorphism groups of quandles and related groups

AU - Bardakov, V.

AU - Nasybullov, T.

AU - Singh, M.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - In this paper we study various questions concerning automorphisms of quandles. For a conjugation quandle (Formula presented.) of a group G we determine several subgroups of (Formula presented.) and find necessary and sufficient conditions for these subgroups to coincide with the whole group (Formula presented.). In particular, we prove that (Formula presented.) if and only if either (Formula presented.) or G is one of the groups (Formula presented.), (Formula presented.) or (Formula presented.). For a big list of Takasaki quandles T(G) of an abelian group G with 2-torsion we prove that the group of inner automorphisms (Formula presented.) is a Coxeter group. We study automorphisms of certain extensions of quandles and determine some interesting subgroups of the automorphism groups of these quandles. Also we classify finite quandles Q with k-transitive action of (Formula presented.) for (Formula presented.).

AB - In this paper we study various questions concerning automorphisms of quandles. For a conjugation quandle (Formula presented.) of a group G we determine several subgroups of (Formula presented.) and find necessary and sufficient conditions for these subgroups to coincide with the whole group (Formula presented.). In particular, we prove that (Formula presented.) if and only if either (Formula presented.) or G is one of the groups (Formula presented.), (Formula presented.) or (Formula presented.). For a big list of Takasaki quandles T(G) of an abelian group G with 2-torsion we prove that the group of inner automorphisms (Formula presented.) is a Coxeter group. We study automorphisms of certain extensions of quandles and determine some interesting subgroups of the automorphism groups of these quandles. Also we classify finite quandles Q with k-transitive action of (Formula presented.) for (Formula presented.).

KW - Automorphism of a quandle

KW - Braid group

KW - Coxeter group

KW - Enveloping group

KW - Quandle

UR - http://www.scopus.com/inward/record.url?scp=85048252730&partnerID=8YFLogxK

U2 - 10.1007/s00605-018-1202-y

DO - 10.1007/s00605-018-1202-y

M3 - Article

AN - SCOPUS:85048252730

VL - 189

SP - 1

EP - 21

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 1

ER -

ID: 13924700