Re: [math-fun] non-square products of squares?

On Fri, 26 Sep 2003, Dan Hoey wrote: >

Here's a poser that came up while I was writing the code to search for nonsquare products. Can it ever happen that (a,b,ab,ba)=(square,square,square,nonsquare)? I can prove it's impossible for finite groups, but what about infinite?

It can't happen, because ba is conjugate to ab, and so if one is a square, so is the other. John Conway