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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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | 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| _version_ | 1856543036289318912 |
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| author | Russo, Francesco G. |
| author_facet | Russo, Francesco G. |
| author_sort | Russo, Francesco G. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T08:18:32Z |
| 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. |
| first_indexed | 2025-12-02T15:40:27Z |
| format | Article |
| id | admjournalluguniveduua-article-623 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:40:27Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | 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 |
| 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 |
| title | 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_short | A generalization of groups with many almost normal subgroups |
| title_sort | generalization of groups with many almost normal subgroups |
| topic | Dietzmann classes anti-\(\mathfrak{X}C\)-groups groups with \(\mathfrak{X}\)-classes of conjugate subgroups Chernikov groups 20C07 20D10 20F24 |
| topic_facet | Dietzmann classes anti-\(\mathfrak{X}C\)-groups groups with \(\mathfrak{X}\)-classes of conjugate subgroups Chernikov groups 20C07 20D10 20F24 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/623 |
| work_keys_str_mv | AT russofrancescog ageneralizationofgroupswithmanyalmostnormalsubgroups AT russofrancescog generalizationofgroupswithmanyalmostnormalsubgroups |