Hey there,

I'm having a bit of trouble with a practise question from my abstract algebra class.

The question is:

Let in (1 2 3 4 5 6) in . Show that is a group using the operation of . Is G abelian? How many elements of G satisfy and ?

I said that the operation of is closed and associative, that every element in has an inverse, and that . I think this is enough to show that G is a group. However, I'm not sure what to do for the abelian or last part. I know that multiplication of disjoint cycles is abelian, but the elements in G that aren't the identity aren't disjoint. I'm kind of lost.

Any hints?