Stacked bases for a pair of homogeneous completely decomposable groups with bounded quotient

Abstract

Let A be a homogeneous completely decomposable torsion free group of infinite rank κ and let X be a torsion free abelian group containing A such that the quotient X/A is bounded. We show that there exist stacked bases for X and A, i.e. there exist b _i ∈ X (i ∈ κ) and d _i ∈ ℤ (i ∈ κ) such that $X = \mathop \oplus \limits_{i \in k} \left\langle {{b_i}} \right\rangle _*^X$ and $A = \mathop \oplus \limits_{i \in k} {d_i}\left\langle {{b_i}} \right\rangle _*^A$. This proves a stacked bases theorem for pairs of homogeneous completely decomposable torsion free abelian groups of infinite rank with bounded quotient.

Supported by a project No. G-0294–081.06/93 of the German-Israeli Foundation for Scientific Research & Development and the Deutsche Akademische Austauschdienst (DAAD).

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