- 2 Let F Be A Field Let G Be The Set Of Functions F F F Of The Form F X Ax B Where A B E F With A 0 A Show Tha 1 (129.69 KiB) Viewed 28 times
2. Let F be a field. Let G be the set of functions f F F of the form f(x) = ax + b where a, b E F with a 0. (a) Show that G is a group with the group multiplication being composition of functions (sometimes this is called the ax + b group). (b) If F is a finite field with q elements, find G. (If q = 5, this gives an explicit construction of a transitive subgroup of S5 with 20 elements). (c) Let f(x) = x5 – 2. Find the Galois group of f over Q. (You may use without proof the fact that there is a unique up to isomorphism transitive subgroup of S5 with 20 elements).