Descent principle in modular Galois theory (Q5947469)

The authors prove that some of the general linear groups \(\text{GL}(m,q)\) occur as Galois groups over some fields of positive characteristic. This is done by starting with a vectorial \(q\)-polynomial of \(q\)-degree \(m\) with Galois group \(\text{GL}(m,q)\) and then enlarging its Galois group to \(\text{GL}(m,q^n)\) by forming its generalized iterative relative to an auxiliary irreducible polynomial of degree \(n.\) Also, the Cameron-Kantor classification of two-transitive linear groups is used.