Order-dominated subgroup: Difference between revisions

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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>.
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==

Revision as of 21:57, 22 February 2009

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Template:Finite subgroup property

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∈G such that gHg−1≤K.

Relation with other properties

Stronger properties

Weaker properties

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