6. Homomorphisms and Isomorphisms

Isomorphism Ideas — Quiz

Test your understanding of isomorphism ideas with 5 practice questions.

Practice Questions

Question 1

Which statement best describes an isomorphism between two groups?

Question 2

If two finite groups are isomorphic, what must be true?

Question 3

Which map is an isomorphism from $(\mathbb{Z}_4,+)$ to $(\{1,-1,i,-i\},\cdot)$?

Question 4

What is the kernel of an isomorphism $f:G\to H$?

Question 5

If $f:G\to H$ is an isomorphism, what is $\operatorname{Im}(f)$?