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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Бібліографічні деталі
Дата:2018
Автор: Russo, Francesco G.
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 oai:ojs.admjournal.luguniv.edu.ua:article-623
record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua: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
institution Algebra and Discrete Mathematics
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
work_keys_str_mv AT russofrancescog ageneralizationofgroupswithmanyalmostnormalsubgroups
AT russofrancescog generalizationofgroupswithmanyalmostnormalsubgroups
first_indexed 2024-04-12T06:25:45Z
last_indexed 2024-04-12T06:25:45Z
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