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## Homework Statement

Find all of the subgroups of Z

_{3}x Z

_{3}

## Homework Equations

Z

_{3}x Z

_{3}is isomorphic to Z

_{9}

## The Attempt at a Solution

x = (0,1,2,3,4,5,6,7,8)

<x

^{0}> or just <0> = {0}

<1> = {identity}

<2> = {0,2,4,6} also wasn't sure if I did this one correctly x o x for x

^{2}

<3> = {0,3,6}

and so on until I got

<8> = {0,8}

<9> = {0}

I feel like I might be completely wrong but is this even a cyclic group, and do I need to approach finding the subgroups differently? Thanks