Pure braid group:P3

Definition
This group is the member of family::pure braid group of degree, denoted $$P_3$$. It is a subgroup of braid group:B3 comprising those braids that induce the identity permutation. In other words, it is the kernel of the natural homomorphism from $$B_3$$ to symmetric group:S3 that sends each braid to its induced permutation.

The group can also be defined by the following presentation: