A generalization of groups with many almost normal subgroups
A subgroup \(H\) of a group \(G\) is called almost normal in \(G\) if it has finitely many conjugates in \(G\). A classic result of B. H. Neumann informs us that \(|G:\mathbf{Z}(G)|\) is finite if and only if each \(H\) is almost normal in \(G\). Starting from this result, we investigate the structu...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/623 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| id |
admjournalluguniveduua-article-623 |
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admjournalluguniveduua-article-6232018-04-04T08:18:32Z A generalization of groups with many almost normal subgroups Russo, Francesco G. Dietzmann classes; anti-\(\mathfrak{X}C\)-groups; groups with \(\mathfrak{X}\)-classes of conjugate subgroups; Chernikov groups 20C07; 20D10; 20F24 A subgroup \(H\) of a group \(G\) is called almost normal in \(G\) if it has finitely many conjugates in \(G\). A classic result of B. H. Neumann informs us that \(|G:\mathbf{Z}(G)|\) is finite if and only if each \(H\) is almost normal in \(G\). Starting from this result, we investigate the structure of a group in which each non-finitely generated subgroup satisfies a property, which is weaker to be almost normal. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/623 Algebra and Discrete Mathematics; Vol 9, No 1 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/623/158 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-04-04T08:18:32Z |
| collection |
OJS |
| language |
English |
| topic |
Dietzmann classes anti-\(\mathfrak{X}C\)-groups groups with \(\mathfrak{X}\)-classes of conjugate subgroups Chernikov groups 20C07 20D10 20F24 |
| spellingShingle |
Dietzmann classes anti-\(\mathfrak{X}C\)-groups groups with \(\mathfrak{X}\)-classes of conjugate subgroups Chernikov groups 20C07 20D10 20F24 Russo, Francesco G. A generalization of groups with many almost normal subgroups |
| topic_facet |
Dietzmann classes anti-\(\mathfrak{X}C\)-groups groups with \(\mathfrak{X}\)-classes of conjugate subgroups Chernikov groups 20C07 20D10 20F24 |
| format |
Article |
| author |
Russo, Francesco G. |
| author_facet |
Russo, Francesco G. |
| author_sort |
Russo, Francesco G. |
| title |
A generalization of groups with many almost normal subgroups |
| title_short |
A generalization of groups with many almost normal subgroups |
| title_full |
A generalization of groups with many almost normal subgroups |
| title_fullStr |
A generalization of groups with many almost normal subgroups |
| title_full_unstemmed |
A generalization of groups with many almost normal subgroups |
| title_sort |
generalization of groups with many almost normal subgroups |
| description |
A subgroup \(H\) of a group \(G\) is called almost normal in \(G\) if it has finitely many conjugates in \(G\). A classic result of B. H. Neumann informs us that \(|G:\mathbf{Z}(G)|\) is finite if and only if each \(H\) is almost normal in \(G\). Starting from this result, we investigate the structure of a group in which each non-finitely generated subgroup satisfies a property, which is weaker to be almost normal. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/623 |
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AT russofrancescog ageneralizationofgroupswithmanyalmostnormalsubgroups AT russofrancescog generalizationofgroupswithmanyalmostnormalsubgroups |
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2025-12-02T15:40:27Z |
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2025-12-02T15:40:27Z |
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1850412166521290752 |