$Groups with many generalized $FC$-subgroup$

Groups with many generalized $FC$-subgroup

Let $FC^0$ be the class of all finite groups, and for each non-negative integer $m$ define by induction the group class $FC^{m+1}$ consisting of all groups $G$ such that the factor group $G/C_G(x^G)$ has the property $FC^m$ for all elements $x$ of $G$. Clearly, $FC^1$ is the class...

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Date:	2018
Main Authors:	Russo, Alessio, Vincenzi, Giovanni
Format:	Article
Language:	English
Published:	Lugansk National Taras Shevchenko University 2018
Subjects:	Conjugacy class $FC$-groups normalizer subgroup subnormal subgroup 20F24
Online Access:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/802
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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-802
record_format	ojs
spelling	oai:ojs.admjournal.luguniv.edu.ua:article-8022018-04-04T08:49:22Z Groups with many generalized $FC$-subgroup Russo, Alessio Vincenzi, Giovanni Conjugacy class, $FC$-groups, normalizer subgroup, subnormal subgroup 20F24 Let $FC^0$ be the class of all finite groups, and for each non-negative integer $m$ define by induction the group class $FC^{m+1}$ consisting of all groups $G$ such that the factor group $G/C_G(x^G)$ has the property $FC^m$ for all elements $x$ of $G$. Clearly, $FC^1$ is the class of $FC$-groups and every nilpotent group with class at most $m$ belongs to $FC^m$. The class of $FC^m$-groups was introduced in [6]. In this article the structure of groups with finitely many normalizers of non-$FC^m$-subgroups (respectively, the structure of groups whose subgroups either are subnormal with bounded defect or have the property $FC^m$) is investigated. 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/802 Algebra and Discrete Mathematics; Vol 8, No 4 (2009) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/802/332 Copyright (c) 2018 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2018-04-04T08:49:22Z
collection	OJS
language	English
topic	Conjugacy class $FC$-groups normalizer subgroup subnormal subgroup 20F24
spellingShingle	Conjugacy class $FC$-groups normalizer subgroup subnormal subgroup 20F24 Russo, Alessio Vincenzi, Giovanni Groups with many generalized $FC$-subgroup
topic_facet	Conjugacy class $FC$-groups normalizer subgroup subnormal subgroup 20F24
format	Article
author	Russo, Alessio Vincenzi, Giovanni
author_facet	Russo, Alessio Vincenzi, Giovanni
author_sort	Russo, Alessio
title	Groups with many generalized $FC$-subgroup
title_short	Groups with many generalized $FC$-subgroup
title_full	Groups with many generalized $FC$-subgroup
title_fullStr	Groups with many generalized $FC$-subgroup
title_full_unstemmed	Groups with many generalized $FC$-subgroup
title_sort	groups with many generalized $fc$-subgroup
description	Let $FC^0$ be the class of all finite groups, and for each non-negative integer $m$ define by induction the group class $FC^{m+1}$ consisting of all groups $G$ such that the factor group $G/C_G(x^G)$ has the property $FC^m$ for all elements $x$ of $G$. Clearly, $FC^1$ is the class of $FC$-groups and every nilpotent group with class at most $m$ belongs to $FC^m$. The class of $FC^m$-groups was introduced in [6]. In this article the structure of groups with finitely many normalizers of non-$FC^m$-subgroups (respectively, the structure of groups whose subgroups either are subnormal with bounded defect or have the property $FC^m$) is investigated.
publisher	Lugansk National Taras Shevchenko University
publishDate	2018
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/802
work_keys_str_mv	AT russoalessio groupswithmanygeneralizedfcsubgroup AT vincenzigiovanni groupswithmanygeneralizedfcsubgroup
first_indexed	2025-07-17T10:32:57Z
last_indexed	2025-07-17T10:32:57Z
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Groups with many generalized \(FC\)-subgroup

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