  For every group genetic code with finite number of generating and at most
with one defining relation we introduce the braid group of this genetic code.
This construction includes the braid group of Euclidean plane, the braid groups
of closed orientable surfaces, B type groups of Artin-Brieskorn, and allow us
to study all these groups with common point of view. We present some results on
the structure of the braid groups of genetic codes, describe normal form of
words, torsion, and some results on widths of the verbal subgroups. Also we
prove that Scott's system of defining relations for the braid groups of closed
surfaces is contradictory.
