Let G be a group in which a^2=e (the id.) for all elements a of G. Show that G is Abelian.
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Originally Posted by r7iris Let G be a group in which a^2=e (the id.) for all elements a of G. Show that G is Abelian. $\displaystyle (ab)^2 = e$ Expand, $\displaystyle abab=e$ So, $\displaystyle ab=ba$ (since $\displaystyle a^{-1} = a \mbox{ and }b^{-1}=b$).
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