Mikhail V. Neshchadim

Representations of virtual braids by automorphisms and virtual knot groups

In the present paper the representation of the virtual braid group

Compatible Actions and Non-abelian Tensor Products

VB_n

Automorphisms of pure braid groups

into the automorphism group of free product of the free group and free abelian group is constructed. This representation generalizes the previously constructed ones. The fact that these already known representations are not faithful for

Palindromic automorphisms of free nilpotent groups

n \geq 4

Groups of triangular automorphisms of a free associative algebra and a polynomial algebra

is verified. Using representations of

Linearity problem for non-abelian tensor products

VB_n

Exterior and symmetric (co)homology of groups.

, the virtual link group is defined. Also representations of welded braid group

Commutator Subgroups of Virtual and Welded Braid Groups

WB_n

Example of non-linearizable quasi-cyclic subgroup of automorphism group of polynomial algebra

are constructed and the welded link group is defined.

Пример нелинеаризуемой квазициклической подгруппы в группе автоморфизмов алгебры многочленов@@@An Example of a Nonlinearizable Quasicyclic Subgroup in the Automorphism Group of the Polynomial Algebra

For a pair of groups G, H, we study pairs of actions G on H and H on G such that these pairs are compatible. We prove that there are nilpotent group G and some group H such that for \(G \otimes H\) the derivative group [G, H] is equal to G. Also, we prove that if \(\mathbb {Z}_2\) act by inversion on an abelian group A, then the non-abelian tensor product \(A \otimes \mathbb {Z}_2\) is isomorphic to A.