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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 an intersectiontransitively central factor if its intersection with any central factor of the whole group is also a central factor.
Formalisms
In terms of the intersectiontransiter
This property is obtained by applying the intersectiontransiter to the property: central factor
View other properties obtained by applying the intersectiontransiter
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
Metaproperties
Trimness
This subgroup property is trim  it is both trivially true (true for the trivial subgroup) and identitytrue (true for a group as a subgroup of itself).
View other trim subgroup properties  View other trivially true subgroup properties  View other identitytrue subgroup properties