On the cotypeset of torsion-free abelian groups

In this paper the cotypeset of some torsion-free abelian groups of finite rank is studied. In particular, we determine the cotypeset of some rank two groups using the elements of their typesets. Introduction One of the important and known tools in the theory of torsion-free abelian groups is type and the typeset of a group. This set which is determined from the beginning of the the study the torsion-free groups, has allocated many papers which are about the identifying this set for torsion-free groups or applying it to determine the properties of these groups and the rings over them. Problems in this area are very diverse; for example, [3] is devoted to a determination of the representation type of indecomposables in the categories of almost completely decomposable groups, or in [6], the author is tried to construct indecomposable group with an special critical typeset, and some articles as well as [4], which are discussed about the representation of some categories of torsion-free abelian groups, are some of the works, which are done related to type. Moreover, [2], that provides perspectives on classification of almost completely decomposable groups and deals with the rank, regulator quotient and near-isomorphism types, is one of the major sources in [11], which is dealing with indecomposable (1, 2)−groups with regulator quotient of 2010 MSC: 20K15.