On the automorphism groups of Frobenius Groups

TL;DR

This paper investigates the automorphism groups of Frobenius groups, specifically when the kernels are elementary abelian and the complements are cyclic, advancing understanding in this specific class of groups.

Contribution

It provides a solution for the automorphism groups of Frobenius groups with elementary abelian kernels and cyclic complements, a case previously unresolved.

Findings

Determined automorphism groups for the specified Frobenius groups.

Extended the classification of automorphism groups in Frobenius group theory.

Provided explicit descriptions of automorphism structures in the studied cases.

Abstract

This is one of a series papers which aim towards to solve the problem of determining automorphism groups of Frobenius groups. This one solves the problem in the case where the Frobenius kernels are elementary abelian and Frobenius complements are cyclic.