Apply the Fundamental Homomorphism Theorem.

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.

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...lows quickly that µ is a well-defined function. It is also easy to check that µ preserves addition.

(b) If (x,y) belongs to ker (µ), then y 0 (mod 3), so y = 0 ...