On transitivity-like properties for torsion-free Abelian groups
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....
| Published in: | Forum mathematicum Vol. 34, № 4. P. 1081-1094 |
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| Main Author: | |
| Other Authors: | , |
| Format: | Article |
| Language: | English |
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| Online Access: | http://vital.lib.tsu.ru/vital/access/manager/Repository/koha:000997862 Перейти в каталог НБ ТГУ |
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| 001 | koha000997862 | ||
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| 008 | 230310|2022 gw s a eng d | ||
| 024 | 7 | |a 10.1515/forum-2021-0295 |2 doi | |
| 035 | |a koha000997862 | ||
| 040 | |a RU-ToGU |b rus |c RU-ToGU | ||
| 100 | 1 | |a Chekhlov, Andrey R. |9 99171 | |
| 245 | 1 | 0 | |a On transitivity-like properties for torsion-free Abelian groups |c A. R. Chekhlov, P. V. Danchev, P. W. Keef |
| 336 | |a Текст | ||
| 337 | |a электронный | ||
| 504 | |a Библиогр.: 19 назв. | ||
| 520 | 3 | |a 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. | |
| 653 | |a группы без кручения | ||
| 653 | |a вполне транзитивные группы | ||
| 653 | |a сепарабельные группы | ||
| 653 | |a транзитивные группы | ||
| 655 | 4 | |a статьи в журналах |9 879358 | |
| 700 | 1 | |a Danchev, Peter V. |9 433885 | |
| 700 | 1 | |a Keef, Patrick W. |9 852075 | |
| 773 | 0 | |t Forum mathematicum |d 2022 |g Vol. 34, № 4. P. 1081-1094 |x 0933-7741 | |
| 852 | 4 | |a RU-ToGU | |
| 856 | 4 | |u http://vital.lib.tsu.ru/vital/access/manager/Repository/koha:000997862 | |
| 856 | |y Перейти в каталог НБ ТГУ |u https://koha.lib.tsu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=997862 | ||
| 908 | |a статья | ||
| 999 | |c 997862 |d 997862 | ||
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