Difference between revisions of "Order-dominated subgroup"

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(New page: {{wikilocal}} {{subgroup property}} ==Definition== A finite subgroup <math>H</math> of a group <math>G</math> is termed '''order-dominated''' in <math>G</math> if, given any fini...)
 
 
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==Definition==
 
==Definition==
  
A finite [[subgroup]] <math>H</math> of a [[group]] <math>G</math> is termed '''order-dominated''' in <math>G</math> if, given any finite subgroup <math>K</math> of <math>G</math> such that the order of <math>H</math> divides the order of <math>K</math>, there exists <math>g \in G</math> such that <math>gHg^{-1} \le K</math>.
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A [[subgroup]] <math>H</math> of a [[finite group]] <math>G</math> is termed '''order-dominated''' in <math>G</math> if, given any finite subgroup <math>K</math> of <math>G</math> such that the order of <math>H</math> divides the order of <math>K</math>, there exists <math>g \in G</math> such that <math>gHg^{-1} \le K</math>.
  
 
==Relation with other properties==
 
==Relation with other properties==

Latest revision as of 21:57, 22 February 2009

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

A subgroup H of a finite group G is termed order-dominated in G if, given any finite subgroup K of G such that the order of H divides the order of K, there exists g \in G such that gHg^{-1} \le K.

Relation with other properties

Stronger properties

Weaker properties