# Elements of alternating group $A_3$

List all the elements of the alternating group $A_3$ written in cyclic notation.

I come up with

Identity $(1)$ Obviously $(123)$

-

(1) (123) (132)

got it

-

Hint: If a group is cyclic, then find an element that is not the identity and find the group that is generated by that element. That is a subset of your group (and even more so a subgroup, albeit unrelated here). And if the group generated is the size of your desired group (you should know the size of $A_3$), then you have all the elements within your group. If you are unfamiliar with cyclic notation please reference the Wikipedia article.

-
(1) (123) (132) – Jessica Oct 22 '10 at 0:07