# Sh:579

• Göbel, R., & Shelah, S. (1996). GCH implies existence of many rigid almost free abelian groups. In Abelian groups and modules (Colorado Springs, CO, 1995), Vol. 182, Dekker, New York, pp. 253–271.
• Abstract:
We begin with the existence of groups with trivial duals for cardinals \aleph_n (n\in \omega). Then we derive results about strongly \aleph_n-free abelian groups of cardinality \aleph_n (n\in\omega) with prescribed free, countable endomorphism ring. Finally we use combinatorial results of [Sh:108], [Sh:141] to give similar answers for cardinals >\aleph_\omega. As in Magidor and Shelah [MgSh:204], a paper concerned with the existence of \kappa-free, non-free abelian groups of cardinality \kappa, the induction argument breaks down at \aleph_\omega. Recall that \aleph_\omega is the first singular cardinal and such groups of cardinality \aleph_\omega do not exist by the well-known Singular Compactness Theorem (see [Sh:52]).
Bib entry
@incollection{Sh:579,
author = {G{\"o}bel, R{\"u}diger and Shelah, Saharon},
title = {{GCH implies existence of many rigid almost free abelian groups}},
booktitle = {{Abelian groups and modules (Colorado Springs, CO, 1995)}},
series = {Lecture Notes in Pure and Appl. Math.},
volume = {182},
year = {1996},
pages = {253--271},
publisher = {Dekker, New York},
mrnumber = {1415638},
mrclass = {20K20 (03E75 04A30)},
note = {\href{https://arxiv.org/abs/math/0011185}{arXiv: math/0011185}},
arxiv_number = {math/0011185}
}