Solve Abstract Algebra Homomorphism Problems with Step-by-Step Guidance

[tinkerbell]

abstract algebra ...HELP, PLZ!

THIS IS THE PROBLEM: COMPUTE THE INDICATED QUANTITIES FOR THE GIVEN HOMOMORPHISM

KER (PHI) AND PHI(18) FOR PHI: Z -> Z10 (SUBCRIPT) SUCH THAT PHI(1)=6

Can anyone please help me to solve this problem? I don't even know what it's asking for? Don't know where to start.

 

[fzero]

You might want to start out with the definition of homomorphism. In particular you should first decide whether the group structure under addition or multiplication is preserved.

 

[tinkerbell]

thanks...I've found ker=10Z, but to find fi(18), I have no clue. I don't know how to relate fi(1)=6. It must be addition

 

[fzero]

Then what is $$\phi(1+1)$$? You should be able to generate the image of all elements like this.