In this article the authors prove theorem on Lifting for the set of virtual pure braid groups.This theorem says that if they know presentation of virtual pure braid group V P_(4),then they can find presentation of V P...In this article the authors prove theorem on Lifting for the set of virtual pure braid groups.This theorem says that if they know presentation of virtual pure braid group V P_(4),then they can find presentation of V Pnfor arbitrary n>4.Using this theorem they find the set of generators and defining relations for simplicial group T_(*)which was defined in[Bardakov,V.G.and Wu,J.,On virtual cabling and structure of 4-strand virtual pure braid group,J.Knot Theory and Ram.,29(10),2020,1-32].They find a decomposition of the Artin pure braid group P_(n)in semi-direct product of free groups in the cabled generators.展开更多
基金supported by the National Natural Science Foundation of China(No.11971144)the State Contract of the Sobolev Institute of Mathematics+2 种基金SB RAS(No.I.1.5,FWNF-2022-0009)the High-level Scientific Research Foundation of Hebei Provincethe Start-up Research Fund from Yanqi Lake Beijing Institute of Mathematical Sciences and Applications。
文摘In this article the authors prove theorem on Lifting for the set of virtual pure braid groups.This theorem says that if they know presentation of virtual pure braid group V P_(4),then they can find presentation of V Pnfor arbitrary n>4.Using this theorem they find the set of generators and defining relations for simplicial group T_(*)which was defined in[Bardakov,V.G.and Wu,J.,On virtual cabling and structure of 4-strand virtual pure braid group,J.Knot Theory and Ram.,29(10),2020,1-32].They find a decomposition of the Artin pure braid group P_(n)in semi-direct product of free groups in the cabled generators.
