Abnormal subgroups and Carter subgroups in some infinite groups

Abnormal subgroups and Carter subgroups in some infinite groups

Some properties of abnormal subgroups in generalized soluble groups are  considered. In particular, the transitivity of abnormality in metahypercentral groups is proven. Also it is proven that a subgroup \(H\) of a radical group G is abnormal in \(G\) if and only if every intermediate subgroup for \...

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Bibliographic Details
Date:2018
Main Authors: Kurdachenko, L. A., Subbotin, I. Ya.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
abnormal subgroups
pronormal subgroups
Carter subgroups
20E34
20F19
20F22
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/917
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-917
record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua:article-9172018-03-21T07:18:38Z Abnormal subgroups and Carter subgroups in some infinite groups Kurdachenko, L. A. Subbotin, I. Ya. abnormal subgroups, pronormal subgroups, Carter subgroups 20E34, 20F19, 20F22 Some properties of abnormal subgroups in generalized soluble groups are  considered. In particular, the transitivity of abnormality in metahypercentral groups is proven. Also it is proven that a subgroup \(H\) of a radical group G is abnormal in \(G\) if and only if every intermediate subgroup for \(H\) coincides with its normalizer in \(G\). This result extends on radical groups the well-known criterion of abnormality for finite soluble groups due to D. Taunt. For some infinite groups (not only periodic) the existence of Carter subgroups and their conjugation have been also obtained. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/917 Algebra and Discrete Mathematics; Vol 4, No 1 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/917/446 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-03-21T07:18:38Z
collection OJS
language English
topic abnormal subgroups
pronormal subgroups
Carter subgroups
20E34
20F19
20F22
spellingShingle abnormal subgroups
pronormal subgroups
Carter subgroups
20E34
20F19
20F22
Kurdachenko, L. A.
Subbotin, I. Ya.
Abnormal subgroups and Carter subgroups in some infinite groups
topic_facet abnormal subgroups
pronormal subgroups
Carter subgroups
20E34
20F19
20F22
format Article
author Kurdachenko, L. A.
Subbotin, I. Ya.
author_facet Kurdachenko, L. A.
Subbotin, I. Ya.
author_sort Kurdachenko, L. A.
title Abnormal subgroups and Carter subgroups in some infinite groups
title_short Abnormal subgroups and Carter subgroups in some infinite groups
title_full Abnormal subgroups and Carter subgroups in some infinite groups
title_fullStr Abnormal subgroups and Carter subgroups in some infinite groups
title_full_unstemmed Abnormal subgroups and Carter subgroups in some infinite groups
title_sort abnormal subgroups and carter subgroups in some infinite groups
description Some properties of abnormal subgroups in generalized soluble groups are  considered. In particular, the transitivity of abnormality in metahypercentral groups is proven. Also it is proven that a subgroup \(H\) of a radical group G is abnormal in \(G\) if and only if every intermediate subgroup for \(H\) coincides with its normalizer in \(G\). This result extends on radical groups the well-known criterion of abnormality for finite soluble groups due to D. Taunt. For some infinite groups (not only periodic) the existence of Carter subgroups and their conjugation have been also obtained.
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/917
work_keys_str_mv AT kurdachenkola abnormalsubgroupsandcartersubgroupsinsomeinfinitegroups
AT subbotiniya abnormalsubgroupsandcartersubgroupsinsomeinfinitegroups
first_indexed 2025-07-17T10:36:45Z
last_indexed 2025-07-17T10:36:45Z
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