Thread: Group Axioms G4 Associative

Hi!

Could anyone help!

I need to prove G4 associativity for the following group and I know it exists

(Q*, o) where x o y = xy/7.

This group is closed so G1 holds
This group is has an identity e = 7 so G2 holds
This group has an inverses which is 49/x.

Originally Posted by Arron

Hi!

Could anyone help!

I need to prove G4 associativity for the following group and I know it exists

(Q*, o) where x o y = xy/7.

This group is closed so G1 holds
This group is has an identity e = 7 so G2 holds
This group has an inverses which is 49/x.

Associativity is the `easy' one, because you don't really have to think! All you have to do is calculate and and see if they are the same!

So...do this...

Thanks. I assume you mean the following.


x o (y o z) = x/7 o (yz/7)
= xyz/49

(x o y) o z = 1/7(xy/7) o z
= xyz/49

Originally Posted by Arron

Thanks. I assume you mean the following.


x o (y o z) = x/7 o (yz/7)
= xyz/49

(x o y) o z = 1/7(xy/7) o z
= xyz/49

Not quite - - you put in the "/7" as you perform the multiplication, and similarly with the other part.