When I get time I take the time to study a little group theory. I am a flyspeck compared to PH and NCA, but here is one I would like some input to see if I have the idea. I will then post my workings.

"Let G be a group which has the following properties:

1: G has no element of order 2

2: $\displaystyle (xy)^{2}=(yx)^{2}, \forall{(x,y)} \in{G}$

By the way, what are the typings for "for all" and "element of"?.

I tried the ones on my list but they wouldn't work.