On torsion in homology of finite connected quandles

Seung Yeop Yang

doi:10.1142/S0218216521410170

On torsion in homology of finite connected quandles

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

Abstract

It is known that the order of a finite quandle annihilates its reduced quandle homology and the torsion subgroup of its rack homology if the quandle is quasigroup. However, this does not hold in general if a quandle is connected. In this paper, we prove that under a certain condition, the reduced quandle homology and the torsion subgroup of the rack homology of a connected quandle are annihilated by the order of the inner automorphism group of the quandle.

Original language	English
Article number	2141017
Journal	Journal of Knot Theory and its Ramifications
Volume	30
Issue number	14
DOIs	https://doi.org/10.1142/S0218216521410170
State	Published - 1 Dec 2021

Keywords

Connected quandle
quandle inner automorphism group
rack and quandle homology
torsion subgroup

Access to Document

10.1142/S0218216521410170

Cite this

@article{70e02f8905794338bf715c95765bfebb,

title = "On torsion in homology of finite connected quandles",

abstract = "It is known that the order of a finite quandle annihilates its reduced quandle homology and the torsion subgroup of its rack homology if the quandle is quasigroup. However, this does not hold in general if a quandle is connected. In this paper, we prove that under a certain condition, the reduced quandle homology and the torsion subgroup of the rack homology of a connected quandle are annihilated by the order of the inner automorphism group of the quandle.",

keywords = "Connected quandle, quandle inner automorphism group, rack and quandle homology, torsion subgroup",

author = "Yang, {Seung Yeop}",

note = "Publisher Copyright: {\textcopyright} 2021 World Scientific Publishing Company.",

year = "2021",

month = dec,

day = "1",

doi = "10.1142/S0218216521410170",

language = "English",

volume = "30",

journal = "Journal of Knot Theory and its Ramifications",

issn = "0218-2165",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "14",

}

TY - JOUR

T1 - On torsion in homology of finite connected quandles

AU - Yang, Seung Yeop

PY - 2021/12/1

Y1 - 2021/12/1

N2 - It is known that the order of a finite quandle annihilates its reduced quandle homology and the torsion subgroup of its rack homology if the quandle is quasigroup. However, this does not hold in general if a quandle is connected. In this paper, we prove that under a certain condition, the reduced quandle homology and the torsion subgroup of the rack homology of a connected quandle are annihilated by the order of the inner automorphism group of the quandle.

AB - It is known that the order of a finite quandle annihilates its reduced quandle homology and the torsion subgroup of its rack homology if the quandle is quasigroup. However, this does not hold in general if a quandle is connected. In this paper, we prove that under a certain condition, the reduced quandle homology and the torsion subgroup of the rack homology of a connected quandle are annihilated by the order of the inner automorphism group of the quandle.

KW - Connected quandle

KW - quandle inner automorphism group

KW - rack and quandle homology

KW - torsion subgroup

UR - http://www.scopus.com/inward/record.url?scp=85127548821&partnerID=8YFLogxK

U2 - 10.1142/S0218216521410170

DO - 10.1142/S0218216521410170

M3 - Article

AN - SCOPUS:85127548821

SN - 0218-2165

VL - 30

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 14

M1 - 2141017

ER -

On torsion in homology of finite connected quandles

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this