A characterization of soluble groups in which normality is a transitive relation

A subgroup $X$ of‎ ‎a group $G$ is said to be an H-‎subgroup if‎ ‎NG(X) ∩ Xg ≤ X for each element $g$ belonging to $G$‎. ‎In [M‎. ‎Bianchi and e.a.‎, ‎On finite soluble groups in which normality is a transitive relation‎, J‎. ‎Group Theory, ‎ 3 (2000) 147--156.] the authors showed that finite group...

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Main Author:	Giovanni Vincenzi
Format:	Article
Language:	English
Published:	University of Isfahan 2017-03-01
Series:	International Journal of Group Theory
Subjects:	‎$H$-subgroups $T$‎-groups ‎ ‎pronormal subgroups‎ ‎weakly normal subgroups‎ ‎pronorm and H-‎norm of a group
Online Access:	http://ijgt.ui.ac.ir/article_10890_1b9c272898954a2b55df94ab7233e6e9.pdf

id	doaj-e548d0f9a88e465aaa6e7932c14f09fc
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spelling	doaj-e548d0f9a88e465aaa6e7932c14f09fc2020-11-24T21:20:58ZengUniversity of IsfahanInternational Journal of Group Theory2251-76502251-76692017-03-0161212710.22108/ijgt.2017.1089010890A characterization of soluble groups in which normality is a transitive relationGiovanni Vincenzi0University of SalernoA subgroup $X$ of‎ ‎a group $G$ is said to be an H-‎subgroup if‎ ‎NG(X) ∩ Xg ≤ X for each element $g$ belonging to $G$‎. ‎In [M‎. ‎Bianchi and e.a.‎, ‎On finite soluble groups in which normality is a transitive relation‎, J‎. ‎Group Theory, ‎ 3 (2000) 147--156.] the authors showed that finite groups in which every subgroup has the H‎-‎property are exactly soluble groups in which normality is a transitive relation‎. ‎Here we extend this characterization to groups without simple sections‎.http://ijgt.ui.ac.ir/article_10890_1b9c272898954a2b55df94ab7233e6e9.pdf‎$H$-subgroups$T$‎-groups‎ ‎pronormal subgroups‎‎weakly normal subgroups‎‎pronorm and H-‎norm of a group
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Giovanni Vincenzi
spellingShingle	Giovanni Vincenzi A characterization of soluble groups in which normality is a transitive relation International Journal of Group Theory ‎$H$-subgroups $T$‎-groups ‎ ‎pronormal subgroups‎ ‎weakly normal subgroups‎ ‎pronorm and H-‎norm of a group
author_facet	Giovanni Vincenzi
author_sort	Giovanni Vincenzi
title	A characterization of soluble groups in which normality is a transitive relation
title_short	A characterization of soluble groups in which normality is a transitive relation
title_full	A characterization of soluble groups in which normality is a transitive relation
title_fullStr	A characterization of soluble groups in which normality is a transitive relation
title_full_unstemmed	A characterization of soluble groups in which normality is a transitive relation
title_sort	characterization of soluble groups in which normality is a transitive relation
publisher	University of Isfahan
series	International Journal of Group Theory
issn	2251-7650 2251-7669
publishDate	2017-03-01
description	A subgroup $X$ of‎ ‎a group $G$ is said to be an H-‎subgroup if‎ ‎NG(X) ∩ Xg ≤ X for each element $g$ belonging to $G$‎. ‎In [M‎. ‎Bianchi and e.a.‎, ‎On finite soluble groups in which normality is a transitive relation‎, J‎. ‎Group Theory, ‎ 3 (2000) 147--156.] the authors showed that finite groups in which every subgroup has the H‎-‎property are exactly soluble groups in which normality is a transitive relation‎. ‎Here we extend this characterization to groups without simple sections‎.
topic	‎$H$-subgroups $T$‎-groups ‎ ‎pronormal subgroups‎ ‎weakly normal subgroups‎ ‎pronorm and H-‎norm of a group
url	http://ijgt.ui.ac.ir/article_10890_1b9c272898954a2b55df94ab7233e6e9.pdf
work_keys_str_mv	AT giovannivincenzi acharacterizationofsolublegroupsinwhichnormalityisatransitiverelation AT giovannivincenzi characterizationofsolublegroupsinwhichnormalityisatransitiverelation
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A characterization of soluble groups in which normality is a transitive relation

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