Hi can someone please help me with this question:
Suppose that His a group in which x^2= e for all x in H.
Prove that H is Abelian.
Thanks
consider $\displaystyle x,y \in G$
then consider $\displaystyle (xy)^2$ and $\displaystyle x^ 2y^2$
$\displaystyle
(xy)^2 = xyxy = e$
$\displaystyle x^2y^2 = xxyy = e$
$\displaystyle \Rightarrow xyxy = xxyy$
Now use properties of Groups to show why the above equation implies that G is Abelian