Title of article :
On the Kernels of Frobenius Groups
Author/Authors :
Darafsheh ، Mohammad R. School of Mathematics, Statistics, and Computer Science, College of Science - University of Tehran , Saydi ، Hadiseh School of Mathematical and Statistical Sciences - North-West University, Mahikeng Campus
Abstract :
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.
Keywords :
Frobenius group , Frobenius complement , Frobenius kernel
Journal title :
Journal of Mahani Mathematical Research Center
Journal title :
Journal of Mahani Mathematical Research Center
