Thread: Group Problem

Prove that if in a group G, then .

My proof so far:

Now (ab)^{2}=a^{2}b^{2} for each a,b \in G,

so

implies

then, there exist a^{-1},b^{-1} in G

(a^-1)(a^2b^2)(b^-1) = (a^-1)(b^2a^2)(b^-1)

ab=ba.

Am I allow to switch the a and b like that?

Originally Posted by tttcomrader

Prove that if in a group G, then .

Have you written the problem correctly?
Or should it be ???

If you do mean that then:

Oops, yeah, that is right.

Please see my edit.

Thank you, sir, that is really easy, I really should have gotten it myself.