Finite complete group: Difference between revisions
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* [[Weaker than::Automorphism group of finite simple non-abelian group]] | * [[Weaker than::Automorphism group of finite simple non-abelian group]] | ||
* [[Weaker than::Automorphism group of finite characteristically simply non-abelian group]] | * [[Weaker than::Automorphism group of finite characteristically simply non-abelian group]]: {{proofat|[[Characteristically simple and non-abelian implies automorphism group is complete]]}} | ||
* [[Weaker than::Finite complete solvable group]] | * [[Weaker than::Finite complete solvable group]] | ||
Latest revision as of 15:07, 2 May 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 finite complete group is a finite group that is also a complete group: it satisfies the following two conditions:
- It is a centerless group: its center is trivial.
- It is a group in which every automorphism is inner.
In other words, a finite complete group is a finite group such that the natural map is an isomorphism.
