Originally Posted by

**kimberu** Does this mean that, accordingly, L = the image is an abelian subgroup, so the only possibilities are <1>, <(123)>, <(12)>,<(23)>, <(13)>, and **not **all of H, so P is not onto?

Then, for part (C), does the following map work?

P(0) --> e

P(1, 3, 5, 7, 9, 11) ---> (12)

P(2,4,6, 8,10) ----> e

If so, the way I found it was basically by guessing...I guess what I'm asking is, is there a systematic way to find this sort of thing dealing with the orders of elements? I tried to find a map onto the group of <(123)>, but I couldn't figure that one out.

Thank you!!