Math Help - Automorphisms, if it generates a group

1. Automorphisms, if it generates a group

Consider the automorphisms of k(x) defined by s1(x) = x (the
identity), s2(x) = 1 - x and s3(x) = 1/x. Show that these generate a group
G of order exactly 6 and that the remaining automorphisms are s4(x) = 1 -
(1/x); s5(x) = 1/(1 - x), and s6(x) = x/(x - 1).

2. Originally Posted by dabien
Consider the automorphisms of k(x) defined by s1(x) = x (the
identity), s2(x) = 1 - x and s3(x) = 1/x. Show that these generate a group
G of order exactly 6 and that the remaining automorphisms are s4(x) = 1 -
(1/x); s5(x) = 1/(1 - x), and s6(x) = x/(x - 1).

Ok...and what's the problem? You must show this set's closed under composition, that you have a unit and that every element there has an inverse (wrt composition, of course)....what've you done and where're you stuck?

Tonio