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