Question

find a homomorphism between the additive groups Z3 and Z6
find a homomorphism between the additive groups Z3 and Z6
@Mathematics

Answer 1

Hormomorphism? what is it?

Answer 2

it is an operation preserving function f:G-->H , <G,*1> <H,*2>

Answer 3

For [x] in Z3, define f : Z3 --> Z6 by
\[ [x] \mapsto [2x] \]

Answer 4

Is that b/c the subgroup of Z3 is {0,1,2} and a subgroup of Z6 is {0,2,4}?

Answer 5

No, it's because this is natural imbedding of Z3 in Z6
as in Z3, [1],[2] are of order 3* and [2], [4] are order 3 elements in Z6.
(*I.e., [1] + [1] + [1] = [0], [2] + [2] + [2] = [0])

Answer 6

Ohhh ok. Thanks, that helps a lot.