Braid group:B3

This group is defined as the braid group of degree three, i.e., the group $$B_3$$. Explicitly, it is given by the following presentation:

$$\langle s_1, s_2 \mid s_1s_2s_1 = s_2s_1s_2 \rangle$$

Up to isomorphism, it is also equivalent to the following:


 * The knot group of the trefoil knot.
 * The universal central extension of special linear group:SL(2,Z).

Group properties
Most of the properties below can be explained by the fact that the group admits free group:F2 as a subquotient.