# Sh:1232

- Asgharzadeh, M., Golshani, M., & Shelah, S. (2023).
*Co-Hopfian and boundedly endo-rigid mixed abelian groups*. PACIFIC JOURNAL OF MATHEMATICS. arXiv: 2210.17210 -
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 JOURNAL OF MATHEMATICS}, year = {2023}, note = {\href{https://arxiv.org/abs/2210.17210}{arXiv: 2210.17210}}, arxiv_number = {2210.17210} }