aleph_n-Free abelain group with no non-zero homomorphism Z

TL;DR

This paper constructs aleph_n-free abelian groups with minimal homomorphisms to Z using advanced black box techniques, contributing to the understanding of their endomorphism structures.

Contribution

It introduces a method to build aleph_n-free abelian groups with few homomorphisms to Z, utilizing aleph_n-free (n+1)-dimensional black boxes.

Findings

Constructed aleph_n-free abelian groups with no non-zero homomorphisms to Z

Developed a technique relevant to prescribed endomorphism rings

Demonstrated the applicability of black box methods in group construction

Abstract

For any natural n, we construct an aleph_n-free abelian groups which have few homomorphisms to Z . For this we use ``aleph_n-free (n+1)-dimensional black boxes''. The method is relevant to e.g. construction of aleph_n-free abelian groups with a prescribed endomorphism ring.