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:
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.
I tried to give you a thanks PH, but your button disappears when I try.
What next?.
Anyway, you had an old one I asked about and had forgotten from almost 2 years ago. Cool.
If I may, here is what I done. I think it is similar to what is on the other posting, but I have to admit I didn't look at it in depth.
It is getting late and I do not feel like typing that much at the moment. I will type mine tomorrow. Okey doke.
Here is my workings. I hope it's OK. I will post while I have time this morning. Today is the 4th. Things to do
For ,
, by part 2.
That's
Next, we have:
, by part 1.
that's
Similarly, we get:
Then we get:
since G has no elements of order 2, we get
And , proving that G is abelian.
WHEW!!. There could easily be a typo in all those x's and y's.