Twisted Virtual Braid Group
Valeriy G. Bardakov, Tatyana A. Kozlovskaya, Komal Negi, and Madeti, Prabhakar

TL;DR
This paper explores the structure of the twisted virtual braid group, identifying key subgroups, their generators, relations, and decompositions, including semi-direct products and connections to virtual pure braid groups.
Contribution
It provides explicit generators, relations, and decompositions for the twisted virtual pure braid group and related subgroups, extending the understanding of their algebraic structure.
Findings
$TVP_n$ is a semi-direct product of a subgroup and $bZ_2^n$
$TVB_n$ decomposes as $TVP_n times S_n$
Constructed new epimorphisms and identified kernels with explicit presentations
Abstract
In this paper we study some subgroups and their decompositions in semi-direct product of the twisted virtual braid group . In particular, the twisted virtual pure braid group is the kernel of an epimorphism of onto the symmetric group . We find the set of generators and defining relations for and show that . Further we prove that is a semi-direct product of some subgroup and abelian group . As corollary we get that the virtual pure braid group is a subgroup of . Also, we construct some other epimorphism of onto . Its kernel, is an analogous of . We find its set of generators and defining relations and construct its decomposition in a semi-direct product.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Homotopy and Cohomology in Algebraic Topology
