Subhomomorph-containing subgroup: Difference between revisions
(New page: {{wikilocal}} {{subgroup property}} ==Definition== A subgroup <math>H</math> of a group <math>G</math> is termed a '''subhomomorph-containing subgroup''' if for any subgroup <math>K \le ...) |
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* [[Stronger than::Subisomorph-containing subgroup]] | * [[Stronger than::Subisomorph-containing subgroup]] | ||
* [[Stronger than::Subhomomorph-dominating subgroup]] | * [[Stronger than::Subhomomorph-dominating subgroup]] | ||
* [[Stronger than::Transfer-closed fully characteristic subgroup]] | |||
* [[Stronger than::Intermediately fully characteristic subgroup]] | * [[Stronger than::Intermediately fully characteristic subgroup]] | ||
* [[Stronger than::Fully characteristic subgroup]] | * [[Stronger than::Fully characteristic subgroup]] | ||
* [[Stronger than::Intermediately strictly characteristic subgroup]] | * [[Stronger than::Intermediately strictly characteristic subgroup]] | ||
* [[Stronger than::Strictly characteristic subgroup]] | * [[Stronger than::Strictly characteristic subgroup]] | ||
* [[Stronger than::Transfer-closed characteristic subgroup]] | |||
* [[Stronger than::Intermediately characteristic subgroup]] | * [[Stronger than::Intermediately characteristic subgroup]] | ||
* [[Stronger than::Characteristic subgroup]] | * [[Stronger than::Characteristic subgroup]] | ||
Revision as of 21:56, 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 of a group is termed a subhomomorph-containing subgroup if for any subgroup and any homomorphism of groups , we have .
Relation with other properties
Stronger properties
Weaker properties
- Homomorph-containing subgroup
- Subisomorph-containing subgroup
- Subhomomorph-dominating subgroup
- Transfer-closed fully characteristic subgroup
- Intermediately fully characteristic subgroup
- Fully characteristic subgroup
- Intermediately strictly characteristic subgroup
- Strictly characteristic subgroup
- Transfer-closed characteristic subgroup
- Intermediately characteristic subgroup
- Characteristic subgroup
Metaproperties
Intermediate subgroup condition
YES: This subgroup property satisfies the intermediate subgroup condition: if a subgroup has the property in the whole group, it has the property in every intermediate subgroup.
ABOUT THIS PROPERTY: View variations of this property satisfying intermediate subgroup condition | View variations of this property not satisfying intermediate subgroup condition
ABOUT INTERMEDIATE SUBROUP CONDITION:View all properties satisfying intermediate subgroup condition | View facts about intermediate subgroup condition