On the Kernels of Frobenius Groups

Document Type : Research Paper

Authors

1 School of Mathematics‎, ‎Statistics‎, ‎and Computer Science‎, College of Science‎, University of Tehran‎, Tehran‎, ‎Iran.

2 Pure and Applied Analytics‎, ‎School of Mathematical and Statistical Sciences‎, North-West University‎, Mahikeng Campus‎, ‎Mmabatho‎, ‎South Africa.

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.

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References

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History

  • Receive Date: 08 April 2024
  • Revise Date: 11 June 2024
  • Accept Date: 12 July 2024

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