Math 421/621
Spring 2000
Homework 6
In
this problem set, are fields. denotes the automorphisms of K that fix F. Let denote a primitive 3rd
root of unity.
- Compute the following
automorphism groups:
a)
b) .
c)
d) (G)
- With the notation as
above, let , and let Show that F1
is a subfield of K containing F and that H is a subgroup of
- Prove the freshman’s
dream holds in a field of characteristic p. That is, show that if is a field of
characteristic p and , then
- Prove Wilson’s theorem:
If p is an odd prime, then
- Find all intermediate
fields between:
a)
and
b)
(G) and
And
find all subgroups of:
c)
d)