Galois group
For the algebraic closure formula_34 of a finite field formula_35 of order "q," the Galois group can be computed explicitly. From the fact formula_36 where the automorphisms are given by the Frobenius endomorphism, the Galois group of the algebraic closure of formula_35 is given by the inverse limit of the groups formula_21, so its Galois group is isomorphic to the group of profinite integers formula_39 which gives a computation of the absolute Galois group of a finite field.