Math 721
Spring 2001
Exam 2
a)
If
is the splitting
field of over and , show that acts transitively on the roots of
b)
Show
that if is irreducible of
degree then is a transitive
subgroup of
a)
Show
that is not Galois over
b)
Let
be the splitting
field of the polynomial over Show that is Galois over and compute its
Galois group.
c)
Express
all roots of the polynomial in terms of radicals.
a)
Show
that for some prime
b)
Show
that any element in a finite field can be written as the sum of two squares.