Groups of two-braid virtual knots

Giving a presentation of the group of a 2-braid virtual knot or link, we consider the groups of three families of 2-braid virtual knots. Each of them has a certain feature; for example, we can show: for any positive integer N, there exists a virtual knot group with an element of order N. It is known that the collection of the virtual knot groups is the same as that of the ribbon T-2-knot groups. Using our examples we discuss the relationship among the virtual knot groups and other knot groups such as ribbon S-2-knot groups, S-2-knot groups, T-2-knot groups, and S-3-knot groups.