Left-transitively WNSCDIN-subgroup

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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