Abstract
For some classes of Abelian groups, an answer to the following question is presented: when is the union of homomorphic images of a group a subgroup of another group? In connection with this, the concept of a homomorphically stable group is introduced, and homomorphic stability of groups from different classes of Abelian groups is studied.
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References
L. Fuchs, Infinite Abelian Groups, Vol. 1, Academic Press, New York (1970).
L. Fuchs, Infinite Abelian Groups, Vol. 2, Academic Press, New York (1973).
S. Ya. Grinshpon, “Fully invariant subgroups of Abelian groups and full transitivity,” Fundam. Prikl. Mat., 8, No. 2, 407–473 (2002).
S. Ya. Grinshpon and T. A. Yeltsova, “Homomorphically stable Abelian groups,” Vestn. TGU, 280, 31–33 (2003).
S. Ya. Grinshpon and T. A. Yeltsova, “Homomorphic images of Abelian groups,” Fundam. Prikl. Mat., 13, No. 3, 17–24 (2007).
R. J. Nunke, “Slender groups,” Bull. Am. Math. Soc., 67, 274–275 (1961).
E. Sasiada, “Proof that every countable and reduced torsion-free Abelian group is slender,” Bull. Acad. Polon. Sci., 7, 143–144 (1959).
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 14, No. 5, pp. 67–76, 2008.
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Grinshpon, S.Y., Yeltsova, T.A. Homomorphic stability of Abelian groups. J Math Sci 163, 670–676 (2009). https://doi.org/10.1007/s10958-009-9702-x
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DOI: https://doi.org/10.1007/s10958-009-9702-x