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For any prime power q we determine a polynomial f q (X) ∈ F q (t,u)[X] whose Galois group over F q (t, u) is the Dickson group G 2 (q). The construction uses a criterion and a method due to Matzat.

Explicit realization of the Dickson groups G2(q) as Galois groups

Explicit realization of the Dickson groups G₂(q) as Galois groups