On primitive subgroups of the full affine group of a finite nearfield (Q2731378)

Let \(F\) be a finite nearfield and let \(\Lambda_F\) be the semidirect product of \(F^*\) with \(\Aut F\). The semidirect product \(A(F)\) of \((F,+)\) with \(\Lambda_F\) is called the full affine group over \(F\). It acts naturally on the set \(F\). (In fact this action is two transitive, and therefore primitive.)NEWLINENEWLINENEWLINEWhen \(F\) is a field, the author determines all subgroups inside \(\Lambda_F\) which act irreducibly on \((F,+)\) and which have an Abelian normal subgroup. This is used to determine all primitive subgroups of \(A(F)\). Here the classification of all finite nearfields comes in handy. Notice that for Dickson nearfields \(F\) the group \(F^*\) is a subgroup of \(\Lambda_K\) for some finite field \(K\).