Prove that, if G is a group and each element of G has order at most 2, then G is abelian.

Thanks.

- March 1st 2011, 03:37 AMfeyomiProve that G is abelian given that each element of G has order at most 2.
Prove that, if G is a group and each element of G has order at most 2, then G is abelian.

Thanks. - March 1st 2011, 04:16 AMDrSteve
Since , for all . Now look at the equation

- March 2nd 2011, 08:14 PMJJMC89
is the only element of order .

if then

so

and

so

Therefore such that all elements have order of at most is Abelian.