Frobenius kernel

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Definition

A Frobenius kernel in a finite group is a proper nontrivial complemented normal subgroup that is also centrally closed subgroup: it contains the centralizer of any nontrivial element in it.

Relation with other properties

Weaker properties

• Self-centralizing normal subgroup
• Finite group admitting a fixed-point-free automorphism of prime order: For full proof, refer: Frobenius kernel implies fixed-point-free automorphism of prime order