TITLE: Extension of the Hall-Witt identity
QUESTION [11 upvotes]: Although this question is mostly out of curiosity (as of now), I hope it is nevertheless suitable for MO.

This very recent (and still open) question about the Hall-Witt identity led me to wonder:


Does some related generalization to 4 or more variables exist?


And also, 


Does that then imply a 4 variable (or more) Jacobi like identity?

REPLY [3 votes]: The following article can answer your question: 
https://www.researchgate.net/publication/319957676_A_generalization_of_the_Hall-Witt_identity