Difference between revisions of "Imperfect group"

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(Created page with '{{group property}} ==Definition== A group is termed an '''imperfect group''' if it has no nontrivial quotient group that is a defining ingredient::perfect group. =…')
 
(Stronger properties)
 
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A [[group]] is termed an '''imperfect group''' if it has no nontrivial [[quotient group]] that is a [[defining ingredient::perfect group]].
 
A [[group]] is termed an '''imperfect group''' if it has no nontrivial [[quotient group]] that is a [[defining ingredient::perfect group]].
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==Examples==
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{{group property see examples}}
  
 
==Relation with other properties==
 
==Relation with other properties==
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* [[Weaker than::Nilpotent group]]
 
* [[Weaker than::Nilpotent group]]
 
* [[Weaker than::Solvable group]]
 
* [[Weaker than::Solvable group]]
* [[Weaker than::Hypoabelian group]]
 

Latest revision as of 20:45, 22 March 2012

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

Definition

A group is termed an imperfect group if it has no nontrivial quotient group that is a perfect group.

Examples

VIEW: groups satisfying this property | groups dissatisfying this property
VIEW: Related group property satisfactions | Related group property dissatisfactions

Relation with other properties

Stronger properties