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Link quandles are residually finite. / Bardakov, Valeriy G.; Singh, Mahender; Singh, Manpreet.
в: Monatshefte fur Mathematik, Том 191, № 4, 01.04.2020, стр. 679-690.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
}
TY - JOUR
T1 - Link quandles are residually finite
AU - Bardakov, Valeriy G.
AU - Singh, Mahender
AU - Singh, Manpreet
N1 - Publisher Copyright: © 2019, Springer-Verlag GmbH Austria, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/4/1
Y1 - 2020/4/1
N2 - Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work (Bardakov et al. in Proc Am Math Soc 147:3621–3633, 2019. https://doi.org/10.1090/proc/14488) residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these results and prove that free products of residually finite quandles are residually finite provided their associated groups are residually finite. As associated groups of link quandles are link groups, which are known to be residually finite, it follows that link quandles are residually finite.
AB - Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work (Bardakov et al. in Proc Am Math Soc 147:3621–3633, 2019. https://doi.org/10.1090/proc/14488) residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these results and prove that free products of residually finite quandles are residually finite provided their associated groups are residually finite. As associated groups of link quandles are link groups, which are known to be residually finite, it follows that link quandles are residually finite.
KW - Free product
KW - Free quandle
KW - Irreducible 3-manifold
KW - Link quandle
KW - Residually finite quandle
KW - KNOT
UR - http://www.scopus.com/inward/record.url?scp=85074458192&partnerID=8YFLogxK
U2 - 10.1007/s00605-019-01336-z
DO - 10.1007/s00605-019-01336-z
M3 - Article
AN - SCOPUS:85074458192
VL - 191
SP - 679
EP - 690
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
SN - 0026-9255
IS - 4
ER -
ID: 22337750