On groups $G_{n}^{k}$, braids and Brunnian braids

Group G_{n}^{3} and imaginary generators

“…Then w 123( φ(β)) = (1, 0)(0, 0)(1, 1)(1, 0)(0, 0)(1, 1) = 1 in F 3 4, where i a123 (4) = (N 124 + N 234 , N 134 + N 234 ) mod 2, and β is non trivial braid in P B 3 . Note that the braid β is Brunnian, and w ijk • φ(β) = 1 for Brunnian braids β, that is, w 123 (φ(β)) = 1 (Theorem 3.4 from[5]).…”