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- W3186994304 abstract "We 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 $< mathfrak{p}$ with infinite $mathrm{Tor}_p(G)$, and that in particular there are no infinite reduced abelian $p$-groups of size $< mathfrak{p}$. Secondly, we prove that if $2^{aleph_0} < lambda < lambda^{aleph_0}$, and $G$ is abelian of size $lambda$, then $G$ is not co-Hopfian. Finally, we prove that for every cardinal $lambda$ there is a torsion-free abelian group $G$ of size $lambda$ which is absolutely Hopfian, i.e., $G$ is Hopfian and $G$ remains Hopfian in every forcing extensions of the universe." @default.
- W3186994304 created "2021-08-02" @default.
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- W3186994304 date "2021-07-23" @default.
- W3186994304 modified "2023-09-27" @default.
- W3186994304 title "On the Existence of Uncountable Hopfian and co-Hopfian Abelian Groups" @default.
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