Characterization of a class of torsion-free Abelian groups

This dissertation is devoted to characterizing a class of corank-1 pure subgroups of completely decomposable groups: Bulter groups of the form G(${\cal A}$) = the kernel of the summation map $\Sigma$: A$\sb1$ $\oplus\...\oplus$ A$\sb{\rm n}\to\doubq$, where ${\cal A}$ = (A$\sb1$,$\...$,A$\sb{\rm n}$) is an n-tuple of subgroups of the group of rationals $\doubq$. Specifically, G(${\cal A}$) and G(${\cal B}$) are quasi-isomorphic if and only if there is a sequence to two-vertex exchanges transforming ${\cal A}$ to ${\cal B}$. A dual theorem is given for the class of Bulter groups of the form G (${\cal A}$), where G (${\cal A}$) = (A$\sb{1}\oplus\...\oplus$ A$\sb{\rm n}$) / $\langle\{({\rm a},\...,{\rm a})\mid0\not={\rm a}\in\cap{\rm A\sb{i}}\}\rangle$.