2023/10/06 by Valeriy G. Bardakov, Bardakov, Valeriy G., Tatyana A. Kozlovskaya +5 · 1 citation
Mathematics · #20F05(secondary) #20F05(secondary) 57K12(primary) #57K12(primary) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2310.04154
openalex publication_date 2023/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study some subgroups and their decompositions in semi-direct product of the twisted virtual braid group TVBn. In particular, the twisted virtual pure braid group TVPn is the kernel of an epimorphism of TVBn onto the symmetric group Sn. We find the set of generators and defining relations for TVPn and show that TVBn = TVPn \rtimes Sn. Further we prove that TVPn is a semi-direct product of some subgroup and abelian group ℤ2n. As corollary we get that the virtual pure braid group VPn is a subgroup of TVPn. Also, we construct some other epimorphism of TVBn onto Sn. Its kernel, TVHn is an analogous of TVPn. We find its set of generators and defining relations and construct its decomposition in a semi-direct product.