Abstract
Quasi-homogeneous weakly transitive rank 2 torsion-free groups are described, and any finite rank torsion-free group with strongly indecomposable pure subgroups is shown to be weakly transitive.
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References
A. R. Chekhlov, “On quasi-purely injective torsion-free Abelian groups,” Abelian Groups Modules, 139–153 (1989).
A. R. Chekhlov, “On a class of endotransitive groups,” Math. Notes, 69, 863–867 (2001).
A. R. Chekhlov, “Torsion-free weakly transitive E-Engel Abelian groups,” Math. Notes, 94, 583–589 (2013).
Yu. B. Dobrusin, “On continuations of partial endomorphisms of torsion-free Abelian groups,” Abelian Groups Modules, 31–41 (1985).
Yu. B. Dobrusin, “On continuations of partial endomorphisms of torsion-free Abelian groups,” Abelian Groups Modules, 36–53 (1986).
L. Fuchs, Infinite Abelian Groups, Academic Press, New York (1970, 1973).
B. Goldsmith and L. Strüngmann, “Torsion-free weakly transitive Abelian groups,” Commun. Algebra, 33, No. 4, 1177–1191 (2005).
B. Goldsmith and L. Strüngmann, “Some transitivity results for torsion Abelian groups,” Houston J. Math., 23, 941–957 (2007).
P. A. Krylov, A. V. Mikhalev, and A. A. Tuganbaev, Endomorphism Rings of Abelian Groups, Kluwer Academic, Dordrecht (2003).
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 5, pp. 191–194, 2019.
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Chekhlov, A.R. On Weakly Transitive Torsion-Free Abelian Groups. J Math Sci 259, 515–517 (2021). https://doi.org/10.1007/s10958-021-05643-5
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DOI: https://doi.org/10.1007/s10958-021-05643-5