STACKED BASES FOR HOMOGENEOUS COMPLETELY DECOMPOSABLE GROUPS

Abstract

Generalizing a theorem by P. Hill and C. Megibben, fixing a rational group R, we characterize by numerical invariants R-presentations of a group G, namely, short exact sequences of the form 0 → A → X → G → 0, where A and X are homogeneous completely decomposable groups of the same type R. This characterization sets afloat the class of the “uniquely R-presented groups”. This class is investigated in connection with the extension to arbitrary groups of the Warfield equivalence between categories of torsionfree abelian groups induced by the functors Hom(R, –) and R ⊗ −. As an application, the stacked bases theorem proved by J. Cohen and H. Gluck in 1970 is extended to arbitrary pairs of homogeneous completely decomposable abelian groups of the same type.

^*Supported by Ministero dell‘Universita’ e della Ricerca Scientifica e Tecnologica (COFIN ‘98).

^†Supported by the Graduiertenkolleg Theoretische und Experimentelle Methoden der Reinen Mathematik of Essen University.

Keywords:

• 1991 Mathematics Subject Index: 20K99

Acknowledgments

Notes

^*Supported by Ministero dell‘Universita’ e della Ricerca Scientifica e Tecnologica (COFIN ‘98).

^†Supported by the Graduiertenkolleg Theoretische und Experimentelle Methoden der Reinen Mathematik of Essen University.