- #1

FanofAFan

- 45

- 0

## Homework Statement

Find all the subgroups of Z

_{3}xZ

_{3}

## Homework Equations

## The Attempt at a Solution

So H is a subgroup of G if H is nonempty, closure for a group, and the inverse must be in H.

(identity)

{([0],[0]) ([0],[1]) ([0],[2])}

{([0],[0]) ([1],[0]) ([2],[0])}

{([0],[0]) ([1],[1]) ([2],[2])}

{([0],[0]) ([0],[1]) ([0],[2]) ([1],[0]) ([2],[0]) ([1],[1]) ([2],[2]) ([1],[2]) ([2],[1])}

{([0],[0]) ([1],[2]) ([2],[1])

is there more subgroups or do I have them all