On the socles of fully invariant subgroups of Abelian \(p\)-groups.
type: Item
instance of: scholarly article
title: On the socles of fully invariant subgroups of Abelian \(p\)-groups.
zbMATH Open document ID: 1173.20038
author: Peter Danchev
author: B. Goldsmith
published in: Archiv der Mathematik
publication date: 2009-06-16T00:00:00Z
review text: Reduced Abelian \(p\)-groups are considered. Socle-regular groups are introduced. A reduced Abelian \(p\)-group \(G\) is said to be socle-regular if for all fully invariant subgroups \(F\) of \(G\) there exists an ordinal \(\alpha\) (depending of \(F\)) such that \(F[p]=(p^\alpha G)[p]\). It is proved that every fully transitive group is socle-regular. Some basic properties of socle-regular groups are investigated. The classification of this class of groups is not made in the article.
Mathematics Subject Classification ID: 20K10
Mathematics Subject Classification ID: 20K30
Mathematics Subject Classification ID: 20K27
zbMATH DE Number: 5565246
zbMATH Keywords: reduced Abelian \(p\)-groups
zbMATH Keywords: fully invariant subgroups
zbMATH Keywords: fully transitive groups
zbMATH Keywords: socle-regular groups
reviewed by: Todor Mollov
MaRDI profile type: Publication
full work available at URL: s00013-009-3021-9
OpenAlex ID: W2110931215
DOI: 10.1007/S00013-009-3021-9
description: scientific article; zbMATH DE number 5565246