We show that the virtual singular braid monoid on n strands embeds in a group V SGn, which we call the virtual singular braid group on n strands. The group V SGn contains a normal subgroup V SP Gn of virtual singular pure braids. We show that V SGn is a semi-direct product of V SP Gn and the symmetric group Sn. We provide a presentation for V SP Gn via generators and relations. We also represent V SP Gn as a semi-direct product of n − 1 subgroups and study the structures of these subgroups. These results yield a normal form of words in the virtual singular braid group.
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