On a class of separable Dedekind groups
type: Item
instance of: scholarly article
zbMATH Open document ID: 0988.20019
DOI: 10.1023/A:1010481407371
author: O. O. Odintsova
publication date: 2001-11-04T00:00:00Z
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20E15
zbMATH DE Number: 1668445
zbMATH Keywords: generalized Dedekind groups
zbMATH Keywords: locally solvable groups
zbMATH Keywords: quasicyclic subgroups
zbMATH Keywords: locally finite groups
MaRDI profile type: Publication
full work available at URL: a:1010481407371
OpenAlex ID: W76713826
published in: Ukraïns'kyĭ Matematychnyĭ Zhurnal
title: On a class of separable Dedekind groups
review text: A class of generalized Dedekind groups is described (a Dedekind group is a group in which all subgroups are normal). The author considers locally solvable groups \(G\) with the following restriction on the system of subgroups: all infinite subgroups of \(G\) which are not contained in a fixed proper subgroup \(S\subset G\) are normal (they are denoted as \(H(I\setminus S)\)-groups). It is shown that such groups are either so-called \(H(S)\)-groups (in which all subgroups not contained in \(S\) are normal) or are some extensions of products of quasicyclic groups by \(H(S)\)-groups.
description: scientific article; zbMATH DE number 1668445