On Outer-Commutator Words
Jeremy M. Wilson · Canadian Journal of Mathematics · 1974
Let F be the group freely generated by the countably infinite set X = {x1, x2, . . . ,xi, . . . }. Let w(x1, x2, . . . , xn) be a reduced word representing an element of F and let G be an arbitrary group. Then V(w, G) will denote the set whose elements will be called values of w in G. The subgroup of G generated by V(w, G) will be called the verbal subgroup of G with respect to w and be denoted by w(G).