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10

Part of 2020 Miklós Schweitzer

Problems(1)

degree of irreducible in F_p divides the degree of the splitting field

Source: Miklos Schweitzer 2020, Problem 10

12/1/2020
Let ff be a polynomial of degree nn with integer coefficients and pp a prime for which ff, considered modulo pp, is a degree-kk irreducible polynomial over Fp\mathbb{F}_p. Show that kk divides the degree of the splitting field of ff over Q\mathbb{Q}.
Galois Theoryabstract algebranumber theoryalgebrapolynomial