# Sh:455

• Kojman, M., & Shelah, S. (1995). Universal abelian groups. Israel J. Math., 92(1-3), 113–124.
• Abstract:
We examine the existence of universal elements in classes of infinite abelian groups. The main method is using group invariants which are defined relative to club guessing sequences. We prove, for example:

Theorem: For n\ge 2, there is a purely universal separable p-group in \aleph_n if, and only if, {2^{\aleph_0}}\leq \aleph_n.

• Version 1994-06-16_10 (14p) published version (12p)
Bib entry
@article{Sh:455,
author = {Kojman, Menachem and Shelah, Saharon},
title = {{Universal abelian groups}},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {92},
number = {1-3},
year = {1995},
pages = {113--124},
issn = {0021-2172},
mrnumber = {1357747},
mrclass = {20K10 (03E05 03E75 20A15 20K20)},
doi = {10.1007/BF02762072},
note = {\href{https://arxiv.org/abs/math/9409207}{arXiv: math/9409207}},
arxiv_number = {math/9409207}
}