TY - JOUR

T1 - On the lower central series of some virtual knot groups

AU - Bardakov, Valeriy G.

AU - Nanda, Neha

AU - Neshchadim, Mikhail V.

PY - 2020/8/1

Y1 - 2020/8/1

N2 - We study groups of some virtual knots with small number of crossings and prove that there is a virtual knot with long lower central series which, in particular, implies that there is a virtual knot with residually nilpotent group. This gives a possibility to construct invariants of virtual knots using quotients by terms of the lower central series of knot groups. Also, we study decomposition of virtual knot groups as semi direct product and free product with amalgamation. In particular, we prove that the groups of some virtual knots are extensions of finitely generated free groups by infinite cyclic groups.

AB - We study groups of some virtual knots with small number of crossings and prove that there is a virtual knot with long lower central series which, in particular, implies that there is a virtual knot with residually nilpotent group. This gives a possibility to construct invariants of virtual knots using quotients by terms of the lower central series of knot groups. Also, we study decomposition of virtual knot groups as semi direct product and free product with amalgamation. In particular, we prove that the groups of some virtual knots are extensions of finitely generated free groups by infinite cyclic groups.

KW - Knot group

KW - representation

KW - residually nilpotent group

KW - virtual braid group

KW - virtual knot

KW - LINKS

UR - http://www.scopus.com/inward/record.url?scp=85091820902&partnerID=8YFLogxK

U2 - 10.1142/S0218216520500650

DO - 10.1142/S0218216520500650

M3 - Article

AN - SCOPUS:85091820902

VL - 29

SP - 5DUMNY

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 9

M1 - 2050065

ER -