Mohammad Darafsheh - School of Mathematics‎, ‎Statistics‎, ‎and Computer Science‎, College of Science‎, University of Tehran‎, Tehran‎, ‎Iran.
Hadiseh Saydi - Pure and Applied Analytics‎, ‎School of Mathematical and Statistical Sciences‎, North-West University‎, Mahikeng Campus‎, ‎Mmabatho‎, ‎South Africa.

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.

frobenius group, frobenius complement, frobenius kernel