Determine the group of field automorphisms of GF(4).
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Determine the group of field automorphisms of GF(4).
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- 16. Suppose that is an abelian group with respect to addition, with identity element Define a multiplication in by for all . Show that forms a ring with respect to these operations.Exercises 30. For an arbitrary positive integer, prove that any two cyclic groups of order are isomorphic.9. Suppose that and are subgroups of the abelian group such that . Prove that .
- Let G be a group of order pq, where p and q are primes. Prove that any nontrivial subgroup of G is cyclic.11. Show that defined by is not a homomorphism.Find the group of automorphisms (Galois group) of the following fields E: (a) Q(√3, √5) (b) Q(w), where w is a primitive cube root of unity (c) Q(w), where w is a primitive fifth root of unity