Every braid in formula_2 can be written as a composition of a number of these braids and their inverses. In other words, these three braids generate the group formula_2. To see this, an arbitrary braid is scanned from left to right for crossings; beginning at the top, whenever a crossing of strands formula_31 and formula_32 is encountered, formula_33 or formula_34 is written down, depending on whether strand formula_31 moves under or over strand formula_32. Upon reaching the right end, the braid has been written as a product of the formula_37's and their inverses.