Frobenius groups Fpn

A Frobenius group is a transitive non-regular permutation group such that no non-trivial element fixes more than one point. For every prime power q, the group of affine linear transformations of the finite field 𝔽q
Fq = AGL(1,q) = 𝔽q𝔽q×
is a Frobenius group, and we use the notation Fq to denote these.