Is there a way to picture a group in ones head?
I want to "see" the difference between abelian and non-abelian group.
And if $f$ is a group homomorphism, is there a way to see that $\ker(f)=1\Leftrightarrow f$ is injective?
What about topological groups? All I see is a map between two spaces.
Are there any easy to visualize examples to have in mind?