CrossRef Open Access 2023 1 sitasi

On the existence of uncountable Hopfian and co-Hopfian abelian groups

Gianluca Paolini Saharon Shelah

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Abstrak

AbstractWe deal with the problem of existence of uncountable co-Hopfian abelian groups and (absolute) Hopfian abelian groups. Firstly, we prove that there are no co-Hopfian reduced abelian groups G of size < p with infinite Torp(G), and that in particular there are no infinite reduced abelian p-groups of size < p. Secondly, we prove that if $${2^{{\aleph _0}}} < \lambda < {\lambda ^{{\aleph _0}}}$$ 2 ℵ 0 < λ < λ ℵ 0 , and G is abelian of size λ, then G is not co-Hopfian. Finally, we prove that for every cardinal λ there is a torsion-free abelian group G of size λ which is absolutely Hopfian, i.e., G is Hopfian and G remains Hopfian in every forcing extension of the universe.

Penulis (2)

Gianluca Paolini

Saharon Shelah

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APA MLA BibTeX

Paolini, G., Shelah, S. (2023). On the existence of uncountable Hopfian and co-Hopfian abelian groups. https://doi.org/10.1007/s11856-023-2534-4

Akses Cepat

Lihat di Sumber doi.org/10.1007/s11856-023-2534-4

Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Total Sitasi: 1×
Sumber Database: CrossRef
DOI: 10.1007/s11856-023-2534-4
Akses: Open Access ✓