Question

Showing two groups are or are not isomorphic. Concept question

Answer 1

So, I think I was wasting a lot of time trying to do this on problems today. So for example, if I had:
\[K_{4} \cong \mathbb{Z}_{4}\] and I wanted to prove or disprove this. I know theres a group isomorphism if theres a function thats 1-1, onto, and is a homomorphism. But in terms of proving this......Whats the best way to do so? I feel like I forgot or dont know the faster way to do this. So can someone maybe look at this example and go from there?

Answer 2

*a function from G1 to G2

Answer 3

if you can show one group is abelian, and the other is not. then they are not isomorphic

Answer 4

thats one trick, there are other things preserved by isomorphism