Thanks to those posting help ... but I am still struggling to determine an answer ...

In answer to the question:

"Find all possible homomorphisms between the indicated groups:

:

"

Swlabr writes: (thanks for help by the way!)

"If

:

, then note that there are no elements of order 3 in

. So if

is to map anywhere nontrivially it must map to a copy of

. So do this and see where it takes you."

However as far as I got was as follows:

I can see that the homomorphism

is completely determined by

(

) =

and, since

has order 6 then we have 0(

) | 6

Thus 0(

) is 6, 3,2 or 1 (Correct?)

... but ... what exactly are the next few steps?