𝐺-projective groups

Abstract

Let TF be the category of torsion free abelian groups of finite rank and homomorphisms. For G G in TF let PC ( G ) {\text {PC}}\left ( G \right ) be the projective class in TF generated by { G } \left \{ G \right \} . Theorem. PC ( G ) {\text {PC}}\left ( G \right ) consists exactly of groups of the form P ⊕ F P \oplus F , where F F is finite rank free and P P is G G -projective P ⊕ P ′ ≅ G n P \oplus P’ \cong {G^n} for some positive integer n n ).