Originally Posted by

**skyking** I'm probably missing something very simple here, but I can't figure this one out.

Let $\displaystyle x_{1},...,x_{n}$ be elements in a group $\displaystyle G$.

show that an element of the form $\displaystyle x_{1}x_{2}...x_{n}x_{1}^{-1}x_{2}^{-1}...x_{n}^{-1}$ is a product of $\displaystyle n-1$ commutators.

I tried this with induction on $\displaystyle n$, but that led nowhere and I tried showing how an element of the form $\displaystyle abca^{-1}b^{-1}c^{-1}$ was a product of 2 commutators but i got stuck.

Any hint would be appreciated

SK