By forgetting how the strands twist and cross, every braid on strands determines a permutation on elements. This assignment is onto and compatible with composition, and therefore becomes a surjective group homomorphism from the braid group onto the symmetric group. The image of the braid σ"i" ∈ is the transposition . These transpositions generate the symmetric group, satisfy the braid group relations, and have order 2. This transforms the Artin presentation of the braid group into the Coxeter presentation of the symmetric group: