On a class of groups with many quasinormal subgroups
type: Item
instance of: scholarly article
title: On a class of groups with many quasinormal subgroups
zbMATH Open document ID: 0597.20022
author: Marta Cardin
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1984-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/107948
review text: The author studies the structure of groups G of the following class: If \(\{H_ i\}_{i\in I}\) is a family of subgroups of G such that \(G=<H_ i:\) \(i\in I>\) then for each i,j\(\in I\), any subgroup contained in \(H_ i\vee H_ j\) is quasinormal in G. It is known that a periodic group with this property is metabelian. The author improves the mentioned result in the following way: If \(\sigma\) is a projectivity of the group G into the group \(\bar G\) and \(N\triangleleft G\), then \((N^{\sigma}[N^{\sigma},2\bar G])^{\sigma -1}/N\) is a modular group.
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20E28
Mathematics Subject Classification ID: 06B15
Mathematics Subject Classification ID: 20F50
zbMATH DE Number: 3961947
zbMATH Keywords: quasinormal subgroups
zbMATH Keywords: metabelian groups
zbMATH Keywords: periodic group
zbMATH Keywords: projectivity
zbMATH Keywords: modular group
reviewed by: František Šik
MaRDI profile type: Publication
cites work: Q5577154
cites work: Über das Verhalten der Normalteiler unter Projektivitäten
cites work: Q5654236
cites work: Q3232305
Recommended article: Q3528101
Recommended article: On groups with many almost normal subgroups
Recommended article: Q4307181
Recommended article: ON -QUASINORMAL SUBGROUPS OF FINITE GROUPS
Recommended article: Q4848170
Recommended article: Q4627026
Recommended article: Groups with few non-quasinormal subgroups
Recommended article: On the quasi-normality and subnormality of subgroups of finite groups
Recommended article: On quasinormal subgroups of infinite groups
Recommended article: Q4009307
description: scientific article; zbMATH DE number 3961947