On a problem of Călugăreanu, Chekhlov and Krylov regarding pure endomorphic images of abelian groups

Author:

Keef Patrick W.1

Affiliation:

1. Department of Mathematics , Whitman College , Walla Walla , WA, 99362 , USA

Abstract

Abstract A problem of Călugăreanu, Chekhlov and Krylov asks which abelian groups have the property that all of their pure subgroups that are endomorphic images are necessarily summands. Complete answers are given for the groups in certain classes (for example, the torsion groups). On the other hand, examples are constructed that show a complete solution to the general problem is likely to be quite difficult.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference6 articles.

1. D. Arnold, Finite Torsion-Free Abelian Groups and Rings, Lecture Notes in Math. 931, Springer, Berlin, 1982.

2. L. Fuchs, Infinite Abelian Groups. Vol. I, Academic Press, New York, 1970.

3. L. Fuchs, Infinite Abelian Groups. Vol. II, Academic Press, New York, 1973.

4. G. Călugăreanu, A. Chekhlov and P. Krylov, Subgroups generated by images of endomorphisms of abelian groups and duality, J. Group Theory 21 (2018), no. 5, 885–900.

5. P. Griffith, Infinite Abelian Group Theory, The University of Chicago Press, Chicago, 1970.

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