Abelian

**SubZero** · March 24th 2010, 09:53 AM

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

**Haven** · March 24th 2010, 10:00 AM

consider $x,y \in G$

then consider $(xy)^2$ and $x^ 2y^2$
$<br /> (xy)^2 = xyxy = e$
$x^2y^2 = xxyy = e$
$\Rightarrow xyxy = xxyy$
Now use properties of Groups to show why the above equation implies that G is Abelian

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