# Group homomorphism

Homomorphism

Problem 3:

Define µ : Z4 × Z6 -> Z4 × Z3 by

µ ([x]4,[y]6) = ([x+2y]4,[y]3).

(a) Show that µ is a well-defined group homomorphism.

(b) Find the kernel and image of µ, and apply the fundamental homomorphism theorem.

https://brainmass.com/math/linear-transformation/apply-fundamental-homomorphism-theorem-2420

#### Solution Preview

Please see attached file.

Homomorphism

Problem 3:

Solution:

(a) If y1 y2 (mod 6), then 2y1 - 2y2 is divisible by 12, so

2y1 2y2 (mod 4), and then it ...

#### Solution Summary

This is a proof regarding a well-defined group homomorphism, and shows how to find kernel and image.

$2.19