title: Hall's identity
text: # Hall's identity
  
  In mathematics, Hall's identity may be:
  
  * The Hall–Witt identity $[x,y^{-1},z]^{y}\cdot [y,z^{-1},x]^{z}\cdot [z,x^{-1},y]^{x}=1$
  * The Hall identity [ $[x,y]^2,z]$ = 0 for 2 by 2 matrices, showing that this is a polynomial identity ring
  * The Hall–Petresco identity for groups expressing $x^my^m$ in terms of powers of elements of the descending central series.
  