# Sh:622

• Shelah, S. (2001). Non-existence of universal members in classes of abelian groups. J. Group Theory, 4(2), 169–191.
• Abstract:
We prove that if \mu^+<\lambda=cf(\lambda)<\mu^{\aleph_0}, then there is no universal reduced torsion free abelian group. Similarly if \aleph_0<\lambda< 2^{\aleph_0}. We also prove that if 2^{\aleph_0}<\mu^+<\lambda=cf(\lambda)< \mu^{\aleph_0}, then there is no universal reduced separable abelian p-group in \lambda. (Note: both results fail if \lambda = \lambda^{\aleph_0} or if \lambda is strong limit, cf(\mu)=\aleph_0<\mu).
• Version 2000-08-21_10 (29p) published version (23p)
Bib entry
@article{Sh:622,
author = {Shelah, Saharon},
title = {{Non-existence of universal members in classes of abelian groups}},
journal = {J. Group Theory},
fjournal = {Journal of Group Theory},
volume = {4},
number = {2},
year = {2001},
pages = {169--191},
issn = {1433-5883},
mrnumber = {1812323},
mrclass = {20K27 (03E75 20A15)},
doi = {10.1515/jgth.2001.014},
note = {\href{https://arxiv.org/abs/math/9808139}{arXiv: math/9808139}},
arxiv_number = {math/9808139}
}