Isomorphism invariants for abelian groups

Abstract

Let A = ( A 1 , … , A n ) A= ({A_1},\ldots ,{A_n}) be an n n -tuple of subgroups of the additive group, Q Q , of rational numbers and let G ( A ) G(A) be the kernel of the summation map A 1 ⊕ ⋯ ⊕ A n → ∑ A i {A_1} \oplus \cdots \oplus {A_n} \to \sum \;{A_i} and G [ A ] G[A] the cokernel of the diagonal embedding ∩ A 1 → A 1 ⊕ ⋯ ⊕ A n \cap \,{A_1} \to {A_1} \oplus \cdots \oplus {A_n} . A complete set of isomorphism invariants for all strongly indecomposable abelian groups of the form G ( A ) G(A) , respectively, G [ A ] G[A] , is given. These invariants are then extended to complete sets of isomorphism invariants for direct sums of such groups and for a class of mixed abelian groups properly containing the class of Warfield groups.