Does a group of order 6 have to be abelian WhySolutionYes a

Does a group of order 6 have to be abelian? Why?.

Solution

Yes, a group od order 6 have to abelian.

Let G be an abelian group of order 6.Then G has one element of order 6.

And so, G is cyclic and isomorphic to Z₆.

In general, It is not true that an abelian group of order n has an element of order n.

However in the case of n=6, it is true.