A generalization of the Hall-Witt identity
The Hall-Witt formula \[ [[x_3,x_1^{-1}],x_2]^{x_1}[[x_1,x_2^{-1}],x_3]^{x_2}[[x_2,x_3^{-1}], x_1]^{x_3} = 1 \] is a kind of three-variable identity which is true in every group. In this paper, the Hall-Witt property of a word \(w\) is defined and it is shown how an infinite number of Hall-Witt-type identities in many variables can be generated by \(w\).
scientific article; zbMATH DE number 6808412