Proposition: An abelian group is not isomorphic to an non-abelian group.
I need to prove this proposition and conclude that: $ \Bbb{Z}/8\Bbb{Z},\Bbb{Z}/4\Bbb{Z}\times \Bbb{Z}/2\Bbb{Z},\Bbb{Z}/2\Bbb{Z}\times\Bbb{Z}/2\Bbb{Z}\times\Bbb{Z}/2\Bbb{Z}\not\cong D_4 $ $ \Bbb{Z}/8\Bbb{Z},\Bbb{Z}/4\Bbb{Z}\times \Bbb{Z}/2\Bbb{Z},\Bbb{Z}/2\Bbb{Z}\times\Bbb{Z}/2\Bbb{Z}\times\Bbb{Z}/2\Bbb{Z}\not\cong Q $ ($D_4$ stands for the dihedral group of order eight and $Q$ for the quaternion group of order eight)
But I have no idea how to begin? Can someone give me some hints/tips?