Settings for a study of finite rank Butler groups

A finite rank Butler group G is a torsionfree Abelian groups that is the sum of m rank one subgroups; G is a B(n)-group if n is the maximum number of independent relations between the m subgroups. After the well-known class B(0), the much studied B(1) and the first approaches to B(2), in this paper we generalize some of the tools used before and introduce new ones to work in every B(n). We study some of the relationships between these tools, and while clarifying some basic settings describe an interesting class of indecomposables.