Originally Posted by

**Bernhard** Can anyone please help with the following problem:

Show that $\displaystyle A_4$ and $\displaystyle \mathbb{Z}_2$ X $\displaystyle S_3 $ are not isomorphic.

Be grateful for help.

I note in passing that both groups have order 12 so in that sense they potentially could be isomorphic. Further, they are both non-abelian so we cannot construct an argument that one is abelian and the other is not.

For those who need an update or re-acquainting with $\displaystyle A_4$ I have attached the relevant pages of Gallian: Contemporary Abstract Algebra

For those who need an update or re-acquainting with $\displaystyle S_3$ I have attached the relevant pages of Fraleigh: A First Course in Abstract Algebra

Peter