In the present paper the representation of the virtual braid group V B n 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 n ≥ 4 is verified. Using representations of V B n , the virtual link group is defined. Also representations of welded braid group W B n are constructed and the welded link group is defined.

No abstract

In this paper we study twisted conjugacy classes of the unit element in different groups. A. L. Fel'shtyn and E. V. Troitsky showed that in an abelian group a twisted conjugacy class of the unit element is a subgroup for any automorphism. In this article we study the question about a structure of the groups, where twisted conjugacy class of the unit element is a subgroup for every automorphism (inner automorphism).

No abstract