Difference between revisions of "Finite-extensible implies class-preserving"

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(New page: {{automorphism property implication}} ==Statement== Any finite-extensible automorphism of a finite group is class-preserving automorphism. ==Facts used== * [[Finite-extensi...)
 
(Facts used)
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* [[Finite-extensible implies finite-characteristic-semidirectly extensible]]
 
* [[Finite-extensible implies finite-characteristic-semidirectly extensible]]
* [[Finite-characteristic-semidirectly-extensible implies linearly pushforwardable over prime field]] (where the prime does not divide the order of the group)
+
* [[Finite-characteristic-semidirectly extensible implies linearly pushforwardable over prime field]] (where the prime does not divide the order of the group)
 
* [[Linearly pushforwardable implies class-preserving]] when the field is a [[class-separating field]]
 
* [[Linearly pushforwardable implies class-preserving]] when the field is a [[class-separating field]]
 
* [[Every finite group admits a sufficiently large prime field]]
 
* [[Every finite group admits a sufficiently large prime field]]
 
* [[Sufficiently large implies splitting]], [[splitting implies character-separating]], [[character-separating implies class-separating]]
 
* [[Sufficiently large implies splitting]], [[splitting implies character-separating]], [[character-separating implies class-separating]]

Revision as of 18:02, 24 June 2008

This article gives the statement and possibly, proof, of an implication relation between two automorphism properties. That is, it states that every automorphism satisfying the first automorphism property must also satisfy the second automorphism property
View all automorphism property implications | View all automorphism property non-implications
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Statement

Any finite-extensible automorphism of a finite group is class-preserving automorphism.

Facts used