Difference between revisions of "Homomorph-containing subgroup"

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(New page: {{wikilocal}} {{subgroup property}} ==Definition== A subgroup <math>H</math> of a group <math>G</math> is termed '''homomorph-containing''' if for any <math>\varphi \in \operator...)
 
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==Definition==
 
==Definition==
  
A [[subgroup]] <math>H</math> of a [[group]] <math>G</math> is termed '''homomorph-containing''' if for any <math>\varphi \in \operatornanem{Hom}(H,G)</math>, the image <math>\varphi(H)</math> is contained in <math>H</math>.
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A [[subgroup]] <math>H</math> of a [[group]] <math>G</math> is termed '''homomorph-containing''' if for any <math>\varphi \in \operatorname{Hom}(H,G)</math>, the image <math>\varphi(H)</math> is contained in <math>H</math>.
  
 
==Relation with other properties==
 
==Relation with other properties==

Revision as of 11:28, 19 September 2008

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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 group G is termed homomorph-containing if for any \varphi \in \operatorname{Hom}(H,G), the image \varphi(H) is contained in H.

Relation with other properties

Weaker properties

Facts