(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that phi : Z(50)->Z(15) is a group homomorphism with phi(7)=6.

a) determine phi(x)

b) Determine the image of phi

c) determine the kernel of phi

d) determine (phi^-1)(3))

2. Relevant equations

3. The attempt at a solution

I know how to determine phi: I need to find a multiple of 7 where zero is the remainder. the multiple is 13 . Next I would say 7*13=1 mod 15. => phi(13*7)=phi(1) => 6*13= 78 mod 15 =3. There phi(1)=3. Thus, phi(x)=3*x.

I'm not sure how to find the image and kernel of phi. I think in order to determine Ker phi, you say Ker phi={x|3x =1}={1/3)}. My result for Ker phi seems incorrect

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# Homework Help: Group homomorphism problem

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