# 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. arXiv: math/0011185 MR: 1415638 -
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]). - No downloadable versions available.

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}, mrclass = {20K20 (03E75 04A30)}, mrnumber = {1415638}, mrreviewer = {John D. O'Neill}, publisher = {Dekker, New York}, note = {\href{https://arxiv.org/abs/math/0011185}{arXiv: math/0011185}}, arxiv_number = {math/0011185} }