Sh:1232
- Asgharzadeh, M., Golshani, M., & Shelah, S. (2023). Co-Hopfian and boundedly endo-rigid mixed abelian groups. Pacific J. Math., 327(2), 183–232. arXiv: 2210.17210 DOI: 10.2140/pjm.2023.327.183 MR: 4716470
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Abstract:
For a given cardinal \lambda and a torsion abelian group K of cardinality less than \lambda, we present, under some mild conditions (for example \lambda=\lambda^{\aleph_0}), boundedly endo-rigid abelian group G of cardinality \lambda with Tor(G)=K. Essentially, we give a complete characterization of such pairs (K, \lambda). Among other things, we use a twofold version of the black box. We present an application of the construction of boundedly endo-rigid abelian groups. Namely, we turn to the existing problem of co-Hopfian abelian groups of a given size, and present some new classes of them, mainly in the case of mixed abelian groups. In particular, we give useful criteria to detect when a boundedly endo-rigid abelian group is co-Hopfian and completely determine cardinals \lambda> 2^{\aleph_{0}} for which there is a co-Hopfian abelian group of size \lambda. - Version 2023-10-02_2 (62p)
Bib entry
@article{Sh:1232,
author = {Asgharzadeh, Mohsen and Golshani, Mohammad and Shelah, Saharon},
title = {{Co-Hopfian and boundedly endo-rigid mixed abelian groups}},
journal = {Pacific J. Math.},
fjournal = {Pacific Journal of Mathematics},
volume = {327},
number = {2},
year = {2023},
pages = {183--232},
issn = {0030-8730},
mrnumber = {4716470},
mrclass = {20K30 (03E75 16S50)},
doi = {10.2140/pjm.2023.327.183},
note = {\href{https://arxiv.org/abs/2210.17210}{arXiv: 2210.17210}},
arxiv_number = {2210.17210}
}