Intersection-transitively central factor

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BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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 an intersection-transitively central factor if its intersection with any central factor of the whole group is also a central factor.

Formalisms

In terms of the intersection-transiter

This property is obtained by applying the intersection-transiter to the property: central factor
View other properties obtained by applying the intersection-transiter

Relation with other properties

Stronger properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Central subgroup contained in the center any subgroup of a central subgroup is central and hence a central factor every group satisfies this property in itself, but need not be central Template:Intermedite notions short

Weaker properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Central factor |FULL LIST, MORE INFO

Metaproperties

Metaproperty name Satisfied? Proof Section in this article
trim subgroup property Yes #Trimness

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