Find all homomorphisms ? : Z/6Z ? Z/15Z.

potrefilizx

potrefilizx

Answered question

2022-09-05

Find all homomorphisms ? : Z/6Z ? Z/15Z.

Answer & Explanation

Maleah Lester

Maleah Lester

Beginner2022-09-06Added 12 answers

Let f : Z/6Z -> Z/15Z be such a homomorphism.
f is completely determined by the value of f(1).
Since 6=0=f(0) in Z/6Z then 0=f(0)=f(6)=6f(1) so 6f(1) = 0 mod 15, 15 divides 6f(1) <=> 5 divides f(1), so f(1) must be either 0, 5 or 10.
So there are 3 homomorphisms.

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