On the Kernels of Frobenius Groups

Author(s):

Mohammad Darafsheh * , Hadiseh Saydi

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
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

Language:
English
Published:
Journal of Mahani Mathematical Research, Volume:13 Issue: 2, Summer and Autumn 2024
Pages:
563 to 569
https://www.magiran.com/p2753625