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- Title
On transitivity-like properties for torsion-free Abelian groups.
- Authors
Chekhlov, Andrey R.; Danchev, Peter V.; Keef, Patrick W.
- Abstract
We study some close relationships between the classes of transitive, fully transitive and Krylov transitive torsion-free Abelian groups. In addition, as an application of the achieved assertions, we resolve some old-standing problems, posed by Krylov, Mikhalev and Tuganbaev in their monograph [P. A. Krylov, A. V. Mikhalev and A. A. Tuganbaev, Endomorphism Rings of Abelian Groups, Kluwer Academic, Dordrecht, 2003]. Specifically, we answer Problem 44 from there in the affirmative by constructing a Krylov transitive torsion-free Abelian group which is neither fully transitive nor transitive. This extends to the torsion-free case certain similar results in the p-torsion case. We, alternatively, also expand to the torsion-free version some of the results concerning transitivity, full transitivity and Krylov transitivity in the p-primary case.
- Subjects
ABELIAN groups; ENDOMORPHISMS; MULTIPLY transitive groups; GROUP rings; ENDOMORPHISM rings
- Publication
Forum Mathematicum, 2022, Vol 34, Issue 4, p1081
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/forum-2021-0295