Zur Vertauschbarkeit und Subnormalität von Untergruppen. (On the permutability and subnormality of subgroups)
type: Item
instance of: scholarly article
title: Zur Vertauschbarkeit und Subnormalität von Untergruppen. (On the permutability and subnormality of subgroups)
zbMATH Open document ID: 0673.20012
DOI: 10.1007/BF01198559
author: Rudolf Maier
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: The author considers the following embedding properties of a subgroup X in a finite group G: X is permutable with all, (M) maximal subgroups, \((M^*)\) maximal subgroups of subnormal subgroups containing X, (N) selfnormalizing subgroups, of G respectively. He is able to show that N- embedded groups X are also \(M^*\)-embedded and subnormal (Satz 4.5); its maximal perfect subgroup is normal in G (Satz 4.7). On the other hand for every non-nilpotent group X there is a non-subnormal M-embedding in some G such that \(| G:X|\) is a power of a suitable prime dividing \(| X|\) (Satz 3.3) while for nilpotent groups all M-embeddings are subnormal embeddings (Folgerung 3.4). The situation is explained further by examples.
Mathematics Subject Classification ID: 20D35
Mathematics Subject Classification ID: 20E28
Mathematics Subject Classification ID: 20D25
zbMATH DE Number: 4101455
zbMATH Keywords: maximal subgroups
zbMATH Keywords: subnormal subgroups
zbMATH Keywords: selfnormalizing subgroups
zbMATH Keywords: maximal perfect subgroup
zbMATH Keywords: M-embeddings
zbMATH Keywords: subnormal embeddings
reviewed by: Hermann Heineken
MaRDI profile type: Publication
cites work: Über die \(\Phi\)-Untergruppe endlicher Gruppen
cites work: Q3934684
cites work: Produkte nilpotenter Gruppen
cites work: Sylow-Gruppen und Subnormalteiler endlicher Gruppen
cites work: Endliche metanilpotente Gruppen
cites work: The embedding of quasinormal subgroups in finite groups
cites work: Vertauschbarkeit von Untergruppen und Subnormalität
cites work: Criteria for subnormality in finite groups.
full work available at URL: https://doi.org/10.1007/bf01198559
OpenAlex ID: W1971973069
description: scientific article; zbMATH DE number 4101455