
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
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