Difference between revisions of "Homomorph-containing subgroup"

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(Relation with other properties)
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===Weaker properties===
 
===Weaker properties===
  
 +
* [[Stronger than::Intermediately fully characteristic subgroup]]
 
* [[Stronger than::Fully characteristic subgroup]]
 
* [[Stronger than::Fully characteristic subgroup]]
 
* [[Stronger than::Strictly characteristic subgroup]]
 
* [[Stronger than::Strictly characteristic subgroup]]
 +
* [[Stronger than::Intermediately characteristic subgroup]]
 
* [[Stronger than::Characteristic subgroup]]
 
* [[Stronger than::Characteristic subgroup]]
 
* [[Isomorph-free subgroup]] in case the subgroup is [[co-Hopfian group|co-Hopfian as a group]]: it is not isomorphic to any proper subgroup of itself.
 
* [[Isomorph-free subgroup]] in case the subgroup is [[co-Hopfian group|co-Hopfian as a group]]: it is not isomorphic to any proper subgroup of itself.

Revision as of 11:35, 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