What Are the Relations Among Field Automorphisms in Galois Theory?

[Kate2010]

Homework Statement

Let L = Q(t) be the field of rational functions with one variable over Q. Consider the field automorphisms of L defined by a : t -> 1 - t and b : t -> 1/t . Find the relations.

I will then be using this to find the size and abstract structure of the subgroup G of Aut(L) generated by a and b. But for now, my question is what does it mean by find the relations?

Homework Equations

The Attempt at a Solution

The only relations I can think of are equivalence relations. All I have managed to do with these automorphisms is work out a^2 = id and b^2 = id.

 

[micromass]

Work out

b
ba
bab
baba
babab
bababa
...

Until you get the identity (or something familiar)