Infinite decomposition bases

Abstract

The concept of decomposition basis is essential to the study of the structure of mixed abelian groups. The main theorem of this paper uses invariants previously defined by the author to determine the decomposition bases of a given group. This is used to extend Ulm's theorem for mixed abelian groups to the entire class of affable groups.1. Introduction. The word "group" will mean abelian group throughout. If X is a subset of a group A, [X] denotes the subgroup generated by X. A, (A p ) represents the torsion part (p-component) of the group A, where p is a prime. Z will denote the integers, while Q represents the rationals. Standard terminology (refer to Fuchs