Prove that Z12 is isomorphic to Z3xZ4. [Consider f: Z -> Z3xZ4 given by f(a) = ([a]3, [a]4).]
Added by Crystal S.
Step 1
Our goal is to prove that \(f\) is an isomorphism. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Sri K and 51 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Consider the group ℤ₉ with addition modulo 9. Define the function f : ℤ₉ → ℤ₉ by f(x) = 4x. Prove that f is an isomorphism. You can assume that f is well-defined here.
Adi S.
Prove that Z2 X Z3 is isomorphic to Z6. (Find and define isomorphism.)
Murali J.
Let f : Z12 → Z4 by f([a]12) = [3a]4. (a) Prove that f is a well defined function. (b) Prove that f is not a ring homomorphism. (c) Is f one-to-one? Is f onto? Prove either one of your choice.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD