The first almost free Whitehead group

TL;DR

This paper proves that if a certain large uncountable cardinal admits a kappa-free abelian group that is not Whitehead, then that cardinal must be inaccessible, linking group theory with set-theoretic large cardinals.

Contribution

It establishes a novel connection between the existence of non-Whitehead kappa-free abelian groups and the inaccessibility of the cardinal, under G.C.H.

Findings

kappa must be inaccessible if such a group exists

connects set theory with algebraic group properties

provides constraints on large cardinal assumptions

Abstract

Assume G.C.H. and kappa is the first uncountable cardinal such that there is a kappa-free abelian group which is not a Whitehead (abelian) group. We prove that kappa is necessarily an inaccessible cardinal