Pure subgroup of torsion-free abelian group

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This article describes a property that arises as the conjunction of a subgroup property: pure subgroup with a group property imposed on the ambient group: torsion-free abelian group
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

Definition

A subgroup H of a group G is termed a pure subgroup of torsion-free abelian group if the following equivalent conditions are satisfied:

  1. G is a torsion-free abelian group and H is a pure subgroup of G.
  2. G is a torsion-free abelian group and H is a local powering-invariant subgroup of G.
  3. G is a torsion-free abelian group and the quotient group G/H is also a torsion-free abelian group.

Relation with other properties

Stronger properties