On the Kernels of Frobenius Groups - Mohammad Darafsheh; Hadiseh Saydi (Journal of Mahani Mathematical Research, 2024)
A Frobenius group is a transitive permutation group on a finite set, such that no non-trivial element fixes more than one point and some non-trivial element fixes a point. Using character theory, it is proved that the Frobenius kernel is a normal subgroup of its Frobenius group. In this paper, we present some group-theoretical proofs that the Frobenius kernel is a subgroup of its Frobenius group under certain conditions.