Settings for a study of Butler B(n)-groups

Abstract. Received 17 January 2007 Available online 4 September 2007. Communicated by Gernot Stroth. 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 gen- eralize 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.