Extensions of group retractions

Abstract

In this paper a condition, which is necessary and sufficient, is determined when a retraction of a subgroup H of a torsion-free group G can be extended to a retraction of G. It is also shown that each retraction of a torsion-free abelian group can be uniquely extended to a retraction of its divisible closure.

Keywords

• group retraction
• extending group retractions
• torsion-free abelian group
• divisible closure.