Up: Abstract Algebra
- Let G be a finite group containing a subgroup
H of index p, where p is the smallest prime divisor of |G|.
Prove that H is a normal subgroup of G.
- Prove that every group of order 15 is cyclic.
- Prove that there is no simple group of order 36.
- Prove that Euclidean domains are principal.
- Prove that the maximal ideals of the
are in bijective correspondence with
- Verify that
be a field of order pn, p a prime.
Show that the automorphisms of
form a cyclic group of order n.
- Determine the irreducible polynomial for
- Construct the finite field
of order 9, and find a generator
for the multiplicative group of nonzero elements of
Mark S. Gockenbach