Left-transitively WNSCDIN-subgroup: Difference between revisions

Latest revision as of 00:18, 7 March 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]
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Definition

A subgroup $H$ of a group $K$ is termed left-transitively WNSCDIN in $K$ if, whenever $K$ is a WNSCDIN-subgroup of a group $G$ , $H$ is also WNSCDIN in $G$ .

Formalisms

In terms of the left-transiter

This property is obtained by applying the left-transiter to the property: WNSCDIN-subgroup
View other properties obtained by applying the left-transiter

Relation with other properties

Stronger properties

Characteristic central factor: For full proof, refer: Characteristic central factor of WNSCDIN implies WNSCDIN

Metaproperties

Trimness

This subgroup property is trim -- it is both trivially true (true for the trivial subgroup) and identity-true (true for a group as a subgroup of itself).
View other trim subgroup properties | View other trivially true subgroup properties | View other identity-true subgroup properties

Transitivity

This subgroup property is transitive: a subgroup with this property in a subgroup with this property, also has this property in the whole group.
ABOUT THIS PROPERTY: View variations of this property that are transitive | View variations of this property that are not transitive
ABOUT TRANSITIVITY: View a complete list of transitive subgroup properties|View a complete list of facts related to transitivity of subgroup properties |Read a survey article on proving transitivity

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 * [[Weaker than::Characteristic central factor]]: {{proofat|[[Characteristic central factor of WNSCDIN implies WNSCDIN]]}}
-* [[Weaker than::Isomorph-free subgroup]]
-* [[Weaker than::Isomorph-normal characteristic subgroup]]: {{proofat|[[Isomorph-normal characteristic of WNSCDIN implies WNSCDIN]]}}
-* [[Weaker than::WNSCDIN-relatively weakly closed subgroup]]: {{proofat|[[Weakly closed of WNSCDIN implies WNSCDIN]]}}
-* [[Weaker than::Sub-isomorph-free subgroup]]
-* [[Weaker than::Sub-(isomorph-normal characteristic) subgroup]]
 ==Metaproperties==