Frobenius group

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).

Stronger properties

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