Mathematics — Unit 1 — Test 22

The Frobenius automorphism σ: F_{p^n}→F_{p^n}, σ(a)=a^p has order

Let f∈Q[x] be irreducible of degree 5 with exactly three real roots. Then its Galois group over Q is

If K/F is a finite Galois extension with group G, then |G| equals

Let α be algebraic over F with minimal polynomial m_α(x) of degree d. Then [F(α):F] equals

Over Q, the polynomial x^4+1 is

Let K=Q(√2,√3). Then [K:Q] equals

The splitting field of x^3−2 over Q has degree

If f∈F[x] is separable and irreducible of degree n, then the number of F‑embeddings of F(ξ) into an algebraic closure is

If K/F is finite and separable, then the number of F‑automorphisms of K is