Which proper subsets of $S_3$ for a group under composition?
I'm not really sure how to approach this. I know the four requirements of groups - identity, closure, inverse and associativity.
And I know that $S_3$ comprises:
(abc) (acb) (bac) (bca) (cba) (cab)
How would I begin to identify the subsets here that meet those four requirements? I would appreciate some hints and tips. I don't just want an answer...I need to actually understand how to answer these types of questions.