Quasi-isomorphism invariants for two classes of finite rank Butler groups

Abstract

A complete set of numerical quasi-isomorphism invariants is given for a class of torsion-free abelian groups containing all groups of the form G [ A ] \mathcal {G}[\mathcal {A}] , where A = ( A 1 , … , A n ) \mathcal {A} = ({A_1}, \ldots ,{A_n}) is an n n -tuple of subgroups of the additive rationals and G [ A ] \mathcal {G}[\mathcal {A}] is the cokernel of the diagonal embedding ⋂ A i → ⊕ A i \bigcap {{A_i} \to \oplus {A_i}} . This classification and its dual include, as special cases, earlier classifications of strongly indecomposable groups of the form G [ A ] \mathcal {G}[\mathcal {A}] and their duals.