Frobenius group

This article defines a property that can be evaluated for finite groups (and hence, a particular kind of group property)
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Definition

A Frobenius group is a finite group satisfying the following equivalent conditions:

• It possesses a Frobenius subgroup: a proper, nontrivial malnormal subgroup.
• It possesses a Frobenius kernel: a proper nontrivial complemented normal centrally closed subgroup.
• It can be expressed as the internal semidirect product of a Frobenius kernel (a centrally closed normal subgroup) and a Frobenius subgroup (a proper nontrivial malnormal subgroup).

Relation with other properties

Stronger properties

• Dihedral group of odd degree: A dihedral group $D_{2n}$ where $n$ is odd.
• General affine group:GA(1,q)