hey,

i have this question,

From my notes these groups are written as addition modulo 10 and 8, but this means that they both have different sizes, so no homomorphism can exist right?

This makes me think that maybe its supposed to be multiplication modulo 10 and 8, which gives

Z_{10}= {1,3,7,9}

Z_{8}= {1,3,5,7}

Then

Y(1)=1

Y(3)=3

Y(7)=5

Y(9)=7 Y(9.7)=Y(3)=3

Y(x)=(x-1)(x-3) + x works

Y(7) = 24 + 7 = 7 (since its in Z8)

Y(9) = 57 = 1

But if this is the case, is it even possible to find ALL the homomorphisms?

Do you guys think that this question was just kind of a trick question, to explain why no homomorphism exists between the two groups (under addition modulo) since their sizes are not the same, (would not be 1-1)?