Intersecting subgroups and symmetric commutator subgroups in virtual link groups

Virtual links can be regarded as links embedded in thickened surfaces. Virtual link groups correspond to the fundamental groups of the complement spaces of the virtual links in thickened surfaces. In this paper, we demonstrate that for a virtual link [Formula: see text] with supporting genus [Formula: see text], the complement space of [Formula: see text] is irreducible and forms a [Formula: see text]-space. Furthermore, we establish that under certain hypotheses, there is an isomorphism between the intersecting subgroup and the symmetric commutator subgroup of all normal closures of meridians in the virtual link group.