Free quandles and knot quandles are residually finite

Valeriy G. Bardakov; Mahender Singh; Manpreet Singh

doi:10.1090/proc/14488

Free quandles and knot quandles are residually finite

Valeriy G. Bardakov, Mahender Singh, Manpreet Singh

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

5 Цитирования (Scopus)

Аннотация

In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residual finiteness of quandles arising from residually finite groups (conjugation, core, and Alexander quandles) is established. Further, residual finiteness of automorphism groups of some residually finite quandles is also discussed.

Язык оригинала	английский
Страницы (с-по)	3621-3633
Число страниц	13
Журнал	Proceedings of the American Mathematical Society
Том	147
Номер выпуска	8
DOI	https://doi.org/10.1090/proc/14488
Состояние	Опубликовано - авг 2019

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10.1090/proc/14488

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abstract = "In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residual finiteness of quandles arising from residually finite groups (conjugation, core, and Alexander quandles) is established. Further, residual finiteness of automorphism groups of some residually finite quandles is also discussed.",

keywords = "3-manifold group, Enveloping group, Free quandle, Knot group, Knot quandle, Peripheral subgroup, Residually finite quandle, enveloping group, knot quandle, peripheral subgroup, free quandle, knot group, residually finite quandle",

author = "Bardakov, {Valeriy G.} and Mahender Singh and Manpreet Singh",

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doi = "10.1090/proc/14488",

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Free quandles and knot quandles are residually finite. / Bardakov, Valeriy G.; Singh, Mahender; Singh, Manpreet.

В: Proceedings of the American Mathematical Society, Том 147, № 8, 08.2019, стр. 3621-3633.

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

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T1 - Free quandles and knot quandles are residually finite

AU - Bardakov, Valeriy G.

AU - Singh, Mahender

AU - Singh, Manpreet

PY - 2019/8

Y1 - 2019/8

N2 - In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residual finiteness of quandles arising from residually finite groups (conjugation, core, and Alexander quandles) is established. Further, residual finiteness of automorphism groups of some residually finite quandles is also discussed.

AB - In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residual finiteness of quandles arising from residually finite groups (conjugation, core, and Alexander quandles) is established. Further, residual finiteness of automorphism groups of some residually finite quandles is also discussed.

KW - 3-manifold group

KW - Enveloping group

KW - Free quandle

KW - Knot group

KW - Knot quandle

KW - Peripheral subgroup

KW - Residually finite quandle

KW - enveloping group

KW - knot quandle

KW - peripheral subgroup

KW - free quandle

KW - knot group

KW - residually finite quandle

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U2 - 10.1090/proc/14488

DO - 10.1090/proc/14488

M3 - Article

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VL - 147

SP - 3621

EP - 3633

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 8

ER -

Free quandles and knot quandles are residually finite

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