On Infinite Groups with Given Properties of the Norm of Infinite Subgroups
We investigate the relationship between the norm N G(∞) of infinite subgroups of an infinite group G and the structure of this group. We prove that N G(∞) is Abelian in the nonperiodic case, and a locally finite group is a finite extension of a quasicyclic subgroup if N G(∞) is a non-Dedekind group....
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| Date: | 2001 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4285 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510415732080640 |
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| author | Lyman, F. N. Lukashova, T. D. Лиман, Ф. Н. Лукашова, Т. Д. |
| author_facet | Lyman, F. N. Lukashova, T. D. Лиман, Ф. Н. Лукашова, Т. Д. |
| author_sort | Lyman, F. N. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:25:53Z |
| description | We investigate the relationship between the norm N G(∞) of infinite subgroups of an infinite group G and the structure of this group. We prove that N G(∞) is Abelian in the nonperiodic case, and a locally finite group is a finite extension of a quasicyclic subgroup if N G(∞) is a non-Dedekind group. In both cases, we describe the structure of the group G under the condition that the subgroup N G(∞) has finite index in G. |
| first_indexed | 2026-03-24T02:56:38Z |
| format | Article |
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| id | umjimathkievua-article-4285 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:56:38Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/9f/812915dd0245040891ddc07d870c709f.pdf |
| spelling | umjimathkievua-article-42852020-03-18T20:25:53Z On Infinite Groups with Given Properties of the Norm of Infinite Subgroups Про нескінченні групи із заданими властивостями норми нескінченних підгруп Lyman, F. N. Lukashova, T. D. Лиман, Ф. Н. Лукашова, Т. Д. We investigate the relationship between the norm N G(∞) of infinite subgroups of an infinite group G and the structure of this group. We prove that N G(∞) is Abelian in the nonperiodic case, and a locally finite group is a finite extension of a quasicyclic subgroup if N G(∞) is a non-Dedekind group. In both cases, we describe the structure of the group G under the condition that the subgroup N G(∞) has finite index in G. Вивчається зв'язок між нормою $N_G(∞)$ нескінченних підгруп нескінченної, групи $G$ та будовою цієї групи. Доведено, що в неперіодичному випадку $N_G(∞)$ — абелева, а локально скінченна група є скінченним розширенням квазіциклічної підгрупи якщо $N_G(∞)$ — недедекіндова група. В обох випадках встановлено будову групи $G$ за умови, що підгрупа $N_G(∞)$ має в $G$ скінченний індекс. Institute of Mathematics, NAS of Ukraine 2001-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4285 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 5 (2001); 625-630 Український математичний журнал; Том 53 № 5 (2001); 625-630 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4285/5274 https://umj.imath.kiev.ua/index.php/umj/article/view/4285/5275 Copyright (c) 2001 Lyman F. N.; Lukashova T. D. |
| spellingShingle | Lyman, F. N. Lukashova, T. D. Лиман, Ф. Н. Лукашова, Т. Д. On Infinite Groups with Given Properties of the Norm of Infinite Subgroups |
| title | On Infinite Groups with Given Properties of the Norm of Infinite Subgroups |
| title_alt | Про нескінченні групи із заданими властивостями норми нескінченних підгруп |
| title_full | On Infinite Groups with Given Properties of the Norm of Infinite Subgroups |
| title_fullStr | On Infinite Groups with Given Properties of the Norm of Infinite Subgroups |
| title_full_unstemmed | On Infinite Groups with Given Properties of the Norm of Infinite Subgroups |
| title_short | On Infinite Groups with Given Properties of the Norm of Infinite Subgroups |
| title_sort | on infinite groups with given properties of the norm of infinite subgroups |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4285 |
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