Talk:2.1.5/@comment-71.232.156.126-20120605190208

Your answer for the first part is very slick. An alternative solution would be to start with xyz = 1, then multiply on the right by x to obtain: xyzx = x. Next, multiply on the left by x's inverse, from which we can easily derive the desired result: yzx = 1.

For the second part, it might be helpful to write out an actual counterexample. From what you've already written, it's clear that you'll need to start with a nonabelian group....