Difference between revisions of "Coprime automorphism-faithful characteristic subgroup"

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(New page: {{wikilocal}} {{subgroup property conjunction|characteristic subgroup|coprime automorphism-faithful subgroup}} ==Definition== A subgroup <math>H</math> of a finite group <math>G<...)
 
 
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defined by restriction, then every prime divisor of the order of <math>K</math>, divides the order of <math>G</math>.
 
defined by restriction, then every prime divisor of the order of <math>K</math>, divides the order of <math>G</math>.
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==Relation with other properties==
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===Stronger properties===
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* [[Weaker than::Critical subgroup]]
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===Weaker properties===
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* [[Stronger than::Characteristic subgroup]]
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* [[Stronger than::Coprime automorphism-faithful subgroup]]

Latest revision as of 21:41, 6 July 2008

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: characteristic subgroup and coprime automorphism-faithful subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

A subgroup H of a finite group G is termed copime automorphism-faithful characteristic if every automorphism of G restricts to an automorphism of H (i.e., H is a characteristic subgroup) and if K is the kernel of the map:

\operatorname{Aut}(G) \to \operatorname{Aut}(H)

defined by restriction, then every prime divisor of the order of K, divides the order of G.

Relation with other properties

Stronger properties

Weaker properties