Subgroups of External Direct Products

[moo5003]

Problem "Find all subgroups of order 3 in Z9 x Z3"

Using an external direct product I came out with the elements:

0,0
0,1
0,2
0... to 0,9
1,0
1... to 1,9
2,0
2... to 2,9


With subgroups:

{(0,0),(1,0),(2,0)}
{(0,0),(0,3),(0,6)}
{(0,0),(1,3),(2,6)}
{(0,0),(1,6),(2,3)}

Just looking for some confirmation if I have done this correctly. I was reading my book and it was lacking a definition/example that I felt like I fully understood.

 

[AKG]

This is 99% correct, it's just that you've given subgroups of Z3 x Z9, not Z9 x Z3.

 

[moo5003]

Wow... nice catch. Now I'm wondering if I can just write on top of the page to switch everything to the other side or if I should re-write the page :(.

I'll just write a little snippet about it and then re-write the subgroups. That seems to the best way about fixing this. Thanks for the help.