A lattice characterization of groups with finite torsion-free rank

Abstract

A group G has finite torsion-free rank if it has a series of finite length whose factors are either infinite cyclic or periodic. A lattice-theoretic characterization of groups with finite torsion-free rank is obtained; it follows in particular that the class of such groups is invariant under projectivities. Moreover, a lattice description of radical groups with finite abelian section rank is given.