Frobenius group: Difference between revisions
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===Stronger properties=== | ===Stronger properties=== | ||
* [[Dihedral group of odd degree | * [[Dihedral group]] of odd degree: A dihedral group <math>D_{2n}</math> where <math>n</math> is odd. | ||
* [[General affine group:GA(1,q)]] | * [[General affine group:GA(1,q)]] | ||
Latest revision as of 00:10, 4 September 2009
This article defines a property that can be evaluated for finite groups (and hence, a particular kind of group property)
View other properties of finite groups OR View all group properties
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 where is odd.
- General affine group:GA(1,q)
